urn:taro:tamu.cush.00103 Inventory of the Harry Shultz Vandiver Papers: 1904-1963 Finding aid prepared by Misti Turbeville Cushing Memorial LibraryTexas A & M University
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Vandiver, Harry Shultz, 1882- Inventory of the Harry Shultz Vandiver Papers: 1904-1963 (2 Boxes) 1.0 linear foot. The Harry Shultz Vandiver Papers (1904-1963) contain scholarly mathematical articles published in America and abroad. Included among these are leading contributions on the history of mathematics, as well as the laws of reciprocity, cyclotomic and relative Abelian algebraic fields, and constructive algebraic theories. Other articles contribute to the fields of number theory, finite algebras, fields, rings, and groups. Also included is Fermat's Last Theorem, the article which established Vandiver's international reputation and brought him the prestigious Frank Cole Prize. TAMU MSS 00103 English. Biographical Note

Harry Shultz Vandiver was born on October 21, 1882, in Philadelphia, Pennsylvania. He attended the University of Pennsylvania and was an instructor of mathematics at Cornell University from 1919-1924. He became an associate professor of pure mathematics at the University of Texas in 1924 and was made a full professor in 1935. The university named him Distinguished Professor of Applied Mathematics and Astronomy in 1947 and he retired in 1966. At various times he was a visiting professor at the University of Chicago, Princeton University, the University of Indiana, and Notre Dame University.

Mr. Vandiver received numerous research appointments and won international recognition as well as the Frank Cole Prize of the American Mathematical Society for his paper Fermat's Last Theorem. He was the author of more than 175 professional articles, a member of numerous academic organizations, and at various times the editor of Annals of Math and Journal of Mathematical Analysis and Applications.

Mr. Vandiver was married on July 25, 1923, to Maude Folsmbee Everson. The couple had one son, Frank E. Vandiver, a historian and educator who was named President of the University of A M in 1981. Harry Shultz Vandiver died on January 4, 1973, in Austin, Texas.

 Scope and Content Note

The Harry Shultz Vandiver Papers (1904-1963) contain scholarly mathematical articles published in America and abroad. Included among these are leading contributions on the history of mathematics, as well as the laws of reciprocity, cyclotomic and relative Abelian algebraic fields, and constructive algebraic theories. Other articles contribute to the fields of number theory, finite algebras, fields, rings, and groups. Also included is Fermat's Last Theorem, the article which established Vandiver's international reputation and brought him the prestigious Frank Cole Prize.

 Organization of the Papers

This collection is organized into 1 series.

Series 1. Publications of Harry Shultz Vandiver and Others, 1904-1963. Access

No restrictions.

 Usage Restrictions

Copyright is retained by the authors of items in these papers, or their descendants, as stipulated by United States copyright law.

Online Catalog Terms

This collection is indexed under the following headings in the online catalog of Cushing Memorial Library. Researchers wishing to find related materials should search the catalog under these index terms.

Names Vandiver, Harry Schultz, 1882- Vandiver, Frank Everson, 1925- Subjects Fermat's last theorem. Mathematics.Reciprocity theorems.Cyclotomy.Number theory. Detailed Description of the Collection

Series 1. Publications of Harry Shultz Vandiver and Others, 1904-1963. 1/1 List of Mathematical Publications of H.S. Vandiver, February, 1964. 1/2 Vandiver, H. S., On Some Special Arithmetic Congruences, American Mathematical Monthly,11:1-5, March, 1904. 1/3 Birkoff, Geo. D. and H.S. Vandiver, On the Integral Divisors of a^n-b^n, Annuals of Mathematics, Second Series, 5:173-180, 1904 1/4 Vandiver, H.S., Theory of Finite Algebras, Transactions of the American Mathematical Society, 13:293-304 1912 1/5 Vandiver, H.S., Extension of the Criteria of Wieferich and Mirimanoff in Connection with Fermat's Last Theorem, Journal fur die Reine und Angewandte Matematik, 114:314-318, 1914 1/6 Vandiver, H.S., Note on Fermat's Last Theorem, Transactions of the American Mathematical Society,15:202-204, 1914 1/7 Vandiver, H.S., An Aspect of the Linear Congruence with Applications to the Theory of Fermat's Quotient, Bulletin of the American Mathematical Society,22:61-68, 1915. (Read before the American Mathematical Society, August 4, 1915.) 1/8 Vandiver, H.S., Note on the Distribution of Quadratic Residues, Bulletin of the American Mathematical Society,23:111-114, 1916. 1/9 Vandiver, H.S., Symmetric Functions Formed by Systems of Elements of a Finite Algebra and Their Connection with Fermat's Quotient and Bernoulli's Numbers, Annals of Mathematics, Series 2, 18:105-114, 1916-1917. 1/10 Kircher, Edward, Some Properties of Certain Finite Algebras, American Journal of Mathematics, 39:273-274, 1917 (includes a theorem of H. S. Vandiver). 1/11 Vandiver, H. S., The Generalized Lagrange Indeterminate Congruence for a Composite Ideal Modules, Annals of Mathematics, 18:115-119, 1917. 1/12 Vandiver, H. S., Proof of a Property of the Norm of a Cyclotomic Integer, Bulletin of the American Mathematical Society, 25:221-223, February, 1919. (Read before the American Mathematical Society, 27 April 1918.) 1/13 Vandiver, H. S., On the First Factor of the Class Number of a Cyclotomic Field, Bulletin of the American Mathematical Society, 25:458-461, July 1919. (Read before the American Mathematical Society, 27 April 1918). 1/14 Vandiver, H. S., A Property of Cyclotomic Integers and Its Relation to Germat's Last Theorem, Annals of Mathematics, 21: 73-80, 1919. (Presented to the AAmerican Mathematical Society, December 1914). 1/15 Vandiver, H. S., On Kummer's Memoir of 1857 Concerning Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 6:266-269, May 1920. (Communicated by L. E. Dickson 6 March 1920). 1/16 Vandiver, H. S., On the Class number of the Field and the Second Case of Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 6:416-421. 1/17 Vandiver, H. S., Bachmann on Fermat's Last Theorem, Bulletin of the American Mathematical Society, 2nd Series, 27:373-376, May 1921. 1/18 Vandiver, H. S., Note on Some Results Concerning Fermat's Last Theorem, Bulletin of the American Math Society, 28:258-260, June 1922. 1/19 Vandiver, H. S., On Kummer's Memoir of 1857 Concerning Fermat's Last Theorem, Bulletin of the American Math Society, 28:400-407, November 1922. 1/20 Vandiver, H. S., Volumes II and III of Dickson's History, Bulletin of the American Math Society, 30:65-70, January-February 1924. 1/21 Vandiver, H. S., On Algorithms for the Solution of the Linear Congruence, The American Mathematical Monthly, 31:137-140, March 1924. 1/22 Vandiver, H. S., Methods for Finding Factors of Large Integers, Bulletin of the American Mathematical Society, 30:542-563, November-December 1924. 1/23 Vandiver, H. S., A New Type of Criteria for the First Case of Fermat's Last Theorem, Annals of Mathematics, 26:88-94, 1924-25. (Presented to the American Math Society 7 September 1923). 1/24 Vandiver, H. S., On Sets of Three Consecutive Integers Which Are Quandratic or cubic Residues of Primes, Bulletin of the American Mathematical Society, 31:33-38, January-February 1925. 1/25 Vandiver, H. S., Laws of Reciprocity and the First Case of Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 11:292-298, June 1925. 1/26 Vandiver, H. S., On the Distribution of Quadratic and Higher Residues, Bulletin of American Mathematical Society, 31:346-350, July 1925. 1/27 Vandiver, H. S., A Property of Cyclotomic Integers and Its Relations to Fermat's Last Theorem (2nd paper), Annals of Mathematics, 26:217-232, 1925. 1/28 Vandiver, H. S., On the Power Characters of Units in a Cyclotomic Field, American Journal of Mathematics, 47:140-147, 1925. 1/29 Vandiver, H. S., Note on Trinomial Congruences and the First Case of Fermat's Last Theorem, Annals of Mathematics, 2nd Series, 27:54-56. 1/30 Vandiver, H. S., Summary of Results and Proofs Concerning Fermat's Last Theorem (1st paper), Proceedings of the National Academy of Sciences, 12:106-109, 1926. (Communicated 6 January 1926.) 1/31 Vandiver, H. S., Transformation of the Kummer Criteria in Connection with Fermat's Last Theorem, Annals of Mathematics, 2nd Series, 27:171-176, March 1926. 1/32 Vandiver, H. S., Application of the Theory of Relative Cyclic Fields to Both Cases of Fermat's Last Theorem, Transactions of the American Mathematical Society, 28:554-560, July 1926. 1/33 Vandiver, H. S., Summary of Results and Proofs Concerning Fermat's Last Theorem (Second Note), Proceedings of the National Academy of Sciences, 12:767-772, December 1926. 1/34 Vandiver, H. S., A Criterion That a Cubic Equation Has an Integral Root, American Mathematical Monthly, 33:94-96, 1926. 1/35 Vandiver, H. S., Application of the Theory of Relative Cyclic Fields for Both Cases of Fermat's Last Theorem, Transactions of the American Mathematical Society, 28:554-560. 1/36 Vandiver, H. S., On the Least Multiple of an Integer Expressible as a Definite Quadratic Form, The American Mathematical Monthly, 34:86-88, February 1927. 1/37 Vandiver, H. S., Application of Algebraic Number Theory to Congruences Involving Binomial Coefficients, Annals of Mathematics, 2nd Series, 28:330-332, July 1927. 1/38 Vandiver, H. S., Review of Fueter's Syntheische Zahlentheorie, American Mathematical Monthly, 34:376-378, 1927. 1/39 Vandiver, H. S., Transformations of the Kummer Criteria in Connection with Fermat's Last Theorem (Second Paper), Annals of Mathematics, 28:451-458, 1928. 1/40 Vandiver, H. S., The Extension of the Bernoulli Summation Formula, American Mathematical Monthly, 36:36, January 1929. 1/41 Vandiver, H. S., Algorithms for the Solution of the Quadratic Congruence, American Mathematical Monthly, 36:83-85, February 1929. 1/42 Vandiver, H. S., Summary of Results and Proofs on Fermat's Last Theorem (Fourth Paper), Proceedings of the National Academy of Sciences, 15:108-109, February 1929. 1/43 Vandiver, H. S., Some Theorems Concerning Properly Irregular Cyclotomic Fields, Proceedings of the National Academy of Sciences, 3:202-207, March 1929. 1/44 Vandiver, H. S., A Theorem of Kummer's Concerning the Second Factor of the Class Number of a Cyclotomic Field, Bulletin of the American Mathematical Society, 35:333-335, May-June 1929. 1/45 Vandiver, H. S., On a Theorem of Kummer's Concerning Power Characters of Units in a Cyclotomic Field, Annals of Mathematics, 2nd Series, 30:487-491, August 1921. 1/46 Vandiver, H. S., On the First Case of Fermat's Last Theorem, Annals of Mathematics, 2nd Series, 30:552-558, October 1929. 1/47 Vandiver, H. S., An Algorithm for Transforming Kummer Criteria in Connection with Fermat's Last Theorem, Annals of Mathematics, 2nd Series, 30:559-577, October 1929. 1/48 Vandiver, H. S., Summary of Results and Proof Concerning Fermat's Last Theorem (Third Paper), Proceedings of National Academy of Sciences, 15:43-48, 1929. (Communicated 17 November 1928). 1/49 Vandiver, H. S., On Fermat's Last Theorem, Transactions of the American Mathematical Society, 31:613-642, 1929. 1/50 Stafford, Elizabeth T. and H. S. Vandiver, Determination of Some Properly Irregular Cyclotomic Fields, Proceedings of the National Academy of Sciences, 16:139-150, February 1930. (Communicated 4 January 1929). 1/51 Vandiver, H. S., Summary of Results and Proofs on Fermat's Last Theorem (Fifth Paper), Proceedings of the National Academy of Sciences, 16:298-304, April 1930. (Communicated 10 March 1930). 1/52 Vandiver, H. S., On the Second Factor of the Class Number of a Cyclotomic field, Proceedings of the National Academy of Sciences, 16:743-749, November 1930. 1/53 Vandiver, H. S., On the the Norm-Residue Symbol in the Theory of Cyclotomic Fields, Proceedings of the National Academy of Sciences, 16:740-743, November 1930. (Communicated 18 September 1930). 1/54 Vandiver, H. S., Some Properties of a Certain System of Independent Units in a Cyclotomic Field, Annals of Mathematics, 31:123-125, 1930. 1/55 Vandiver, H. S., A New Theory of the Representation of Integers as Definite Quadratic Forms, Annals of Mathematics, 31:117-122, 1930. 1/56 Vandiver, H. S., Summary of Results and Proofs of Fermat's Last Theorem (Sixth Paper), Proceedings of the National Academy of Sciences, 17:661-673, December 1931. (Communicated 26 October 1931). 1/57 Vandiver, H. S., Note on the Divisors of the Numerators of Bernoulli's Numbers, Proceedings of the National Academy of Sciences, 18:594-597, September 1932. (Dommunicated 28 July 1932). 1/58 Vandiver, H. S., On the Method of Infinite Descent in Connection with Fermat's Last Theorem for Regular Prime Exponents, Commentarii Mathematici Helvetici, 4:1-8, 1932. 1/59 Vandiver, H. S., Review of Nogue's Theoreme de Fermat, Bulletin of American Mathematical Society, 38:794-795, 1932. 1/60 Vandiver, H. S., Fermat's Last Report and the Second Factor in the Cyclotomic Class Number, Bulletin of the American Mathematical Society, 40:118-126, February 1934. 1/61 Vandiver, H. S., On Power Characters in Cyclotomic Fields, Bulletin of the American Mathematical Society, 40:111-117, February 1934. 1/62 Vandiver, H. S., On the Foundations of a Constructive Theory of Discrete Commutative Algebra, Proceedings of the National Academy of Sciences, 20:579-584. 1/63 Vandiver, H. S., A Note of Units in Super-Cyclic Fields, Bulletin of the American Mathematical Society, 40:855-858, December 1934. 1/64 Vandiver, H. S., Note on a Simple Type of Algebra in which the Cancellation Law of Addition Does Not Hold, Bulletin of the American Mathematical Society, 40:914-920, December 1934. 1/65 Vandiver, H. S., On the Foundations of a Constructive Theory of Discrete Commutative Algebra (Second Paper), Proceedings of the National Academy of Sciences, 21:162-165, 1935. 1/66 Vandiver, H. S., Constructive Derivation of the Decomposition-Field of a Polynomial, Annals of Mathematics, 37:1-6, January 1936. 1/67 Vandiver, H. S., On the Ordering of Real Algebraic Numbers by Constructive Methods, Annals of Mathematics, 37:7-16, January 1936. 1/68 Vandiver, H. S., Note on the Associative Distributive Algebra in Which the Commutative Law of Additon Does Not Hold, Bulletin of the American Mathematical Society, 41:857-859, December 1936. 1/69 Vandiver, H. S., On Trinomial Diophantine Equations Connected with the Fermat Relations, Monatshefte fur Mathematik and Physik, 43:317-320, 1936. 1/70 Vandiver, H. S., Note on a Certain Ring-Congruence, Bulletin of the American Mathematical Society, 41:418-423, June 1937. 1/71 Vandiver, H. S., On the Concept of Co-Sets In a Semi-group, Proceedings of the National Academy of Sciences, 23:552-555, October 1937. (Communicated 8 September 1937). 1/72 Vandiver, H. S., On Generalizations of the Numbers of Bernoulli and Euler, Proceedings of the National Academy of Sciences, 23:555-559, October 1937. (Communicated 8 September 1937). 1/73 Vandiver, H. S., On Bernoulli's Numbers and Fermat's Last Theorem, Duke Mathematical Journal, 3:569-584, December 1937. 1/74 Vandiver, H. S., On Criteria Concerning Singular Integers in Cyclotomic Fields, Proceedings of the National Academy of Sciences, 24:330-333, August 1938. 1/75 Vandiver, H. S., On Congruences Involving Sums of Products of Binomial Coefficients, American Mathematical Monthly, 45:369-371, 1938. 2/1 Vandiver, H. S., On Some Simple Types of Semi-Rings, American Mathematical Monthly, 46:22-26, January 1939. 2/2 Vandiver, H. S., On Analogues of the Bernoulli and Allied Numbers, Proceedings of the National Academy of Sciences, 25:197-201, April 1939. (Communicated 21 February 1939). 2/3 Vandiver, H. S., On Bernoulli's Numbers and Fermat's Last Theorem (Second Paper), Duke Mathematical Journal, 5:418-427, June 1939. 2/4 Vandiver, H. S., Certain Congruences Involving the Bernoulli Numbers, Duke Mathematical Journal, 5:548-551, September 1939. 2/5 Vandiver, H. S., On Basis Systems for Groups of Ideal Classes in a Properly Irregular Cyclotomic Field, Proceedings of the National Academy of Sciences, 25:586-591, November 1939. 2/6 Vandiver, H. S., On the Composition of the Group of Ideal Classes in a Properly Irregular Cyclotomic Field, Monatshefte fur Mathematik und Physick, (Festband Ph. Furtwangler), 48:369-380, 1939. 2/7 Vandiver, H. S., On the Imbedding of One Semi-group in Another, with Application to Semi-rings, American Journal of Mathematics, 62:72-78, January 1940. 2/8 Vandiver, H. S., On General Methods for Obtaining Congruences Involving Bernoulli Numbers, Bulletin of the American Mathematical Society, 46:121-123, February 1940. 2/9 Vandiver, H. S., Note on Euler Number Criteria for the First Case of Fermat's Last Theorem, American Journal of Mathematics, 62:79-82, January 1940. 2/10 Vandiver, H. S., The Elements of a Theory of Abstract Discrete Semi-groups, Vierteljahrsschrift der Naturforschenden Gesellschaft in Zurich, 85:71-86, 1940. 2/11 Vandiver, H. S., On Improperly Irregular Cyclotomic Fields, Proceedings of the National Academy of Sciences, 27:77-83, January 1941. 2/12 Vandiver, H. S., Simple Explicit Expressions for Generalized Bernoulli Numbers of the First Order, Duke Mathematical Journal, 8:575-584, September 1941. 2/13 Vandiver, H. S., Review of Diophantische Gleichungen by T. Skolem, Bulletin of the American Mathematical Society, 48:10-15, January 1942. 2/14 Vandiver, H. S., On Formal Exponential Differentiation in Rings, Proceedings of the National Academy of Sciences, 28:24-27, January 1942. 2/15 Vandiver, H. S., Certain Congruence Criteria Connected with Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 28:144-150, April 1942. 2/16 Vandiver, H. S., An Arithmetical Theory of the Bernoulli Numbers, Transactions of the American Mathematical Society, 51:502-531, May 1942. 2/17 Vandiver, H. S., General Congruences Involving the Bernoulli Numbers, Proceedings of the National Academy of Sciences, 28:324-328, August 1942. 2/18 Vandiver, H. S., Some Theorems in Finite Field Theory with Applications to Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 30:362-367, November 1944. 2/19 Vandiver, H. S., On Trinomial Congruences and Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 300:368-370, November 1944. (Communicated 25 September 1944). 2/20 Vandiver, H. S., New Types of Relations in Finite Field Theory, Proceedings of the National Academy of Sciences, 31:50-54, January 1945. 2/21 Vandiver, H. S., Fermat's Quotient and Related Arithmetic Functions, Proceedings of the National Academy of Sciences, 31:50-54, January 1945. 2/22 Vandiver, H. S., On the Numbers of Solutions of Certain Non-homogeneous Equations in a Finite Field, Proceedings of the National Academy of Sciences, 31:170-175, June 1945. 2/23 Vandiver, H. S., New Types of Relations in Finite Field Theory (Second Paper), Proceedings of the National Academy of Sciences, 31:189-194, July 1945. 2/24 Vandiver, H. S., Bernoulli's Numbers and Certain Arithmetic Quotient Functions, Proceedings of the National Academy of Sciences, 31:310-314, September 1945. 2/25 Vandiver, H. S., On the Number of Solutions of Some General Types of Equations in a Finite Field, Proceedings of the National Academy of Sciences, 32:47-52, February 1946. 2/26 Vandiver, H. S., On Classes of Diophantine Equations of Higher Degrees Which Have No Solutions, Proceedings of the National Academy of Sciences, 32:101-106, April 1946. (Communicated 20 February 1946). 2/27 Vandiver, H. S., Cyclotomy and Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 32:317-319, 15 December 1946. (Communicated 23 September 1946). 2/28 Vandiver, H. S., On Some Special Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 32:320-326, 15 December 1946. 2/29 Vandiver, H. S., Fermat's Last Theorem, American Mathematical Monthly, 53:555-578, December 1946. 2/30 Vandiver, H. S., On a p-ADIC Representation of Rings and Abelian Groups, Annals of Mathematics, 48:22-28, January 1947. 2/31 Vandiver, H. S., Limits for the Number of Solutions of Certain General Types of Equations in a Finite Field, Proceedings of the National Academy of Sciences, 33:236-242, 1947. 2/32 Diophantine Analysis, article in 1947 editon of Encyclopedia Britannica, 7:398-400, 1947. 2/33 Fermat's Last Theorem, article in 1947 edition of Encyclopedia Britannica, 9:173-174, 1947. 2/34 Vandiver, H. S., Applications of Cyclotomy to the Theory of Nonhomogeneous Equations in a Finite Field, Proceedings of the National Academy of Sciences, 34:62-66, February 1948. 2/35 Vandiver, H. S., New Types of Congruences Involving Bernoulli Numbers and Fermat's Quotient, Proceedings of the National Academy of Science, 34:103-110, March 1948. 2/36 Vandiver, H. S., Cyclotomic Power Characters and Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 34:196-203, May 1948. 2/37 Vandiver, H. S., On the Existence of Solutions of Certain Equations in a Finite Field, Proceedings of the National Academy of Sciences, 34:258-263, June 1948. 2/38 Vandiver, H. S., Congruence Methods as Applied to Diophantine Analysis, Math Magazine, 22:185-192, 1948. 2/39 Vandiver, H. S., Characters Over Certain Types of Rings with Applications to the Theory of Equations in a Finite Field, Proceedings of the National Academy of Sciences, 35:94-99, February 1949. 2/40 Vandiver, H. S., On Congruence Which Relate the Fermat and Wilson Quotients to the Bernoulli Numbers, Proceedings of the National Academy of Sciences, 35:332-337, June 1949. 2/41 Vandiver, H. S., On the Nature of the Solutions of Certain Equations in a Finite Field, Proceedings of the National Academy of Sciences, 35:481-487, August 1949. 2/42 Vandiver, H. S., On the Number of Solutions of Some Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 35:477-481, August 1949. 2/43 Vandiver, H. S., On the Use of Indeterminates in the Theory of Exponential Sums, Proceedings of the National Academy of Sciences, 35:686-690, December 1949. 2/44 Vandiver, H. S., Quadratic Relations Involving the Numbers of Solutions of Certain Types of Equations in a Finite Field, Proceedings of the National Academy of Sciences, 35:681-685, December 1949. 2/45 Vandiver, H. S., On a Generalization of a Jacobi Exponential Sum Associated with Cyclotomy, Proceedings of the National Academy of Sciences, 36:1-44, 151, February 1950. 2/46 Faircloth, O. B. and H. S. Vandiver, On Multiplicative Properties of a Generalized Jacobi-Cauchy Cyclotomic Sum, Proceedings of the National Academy of Sciences, 36:260-267, April 1950. 2/47 Faircloth, O. B. and H. S. Vandiver, On Certain Diophantine Equations in Rings and Fields, Proceedings of the National Academy of Sciences, 38:52-57, January 1952. 2/48 Vandiver, H. S., On Cyclotomy and Extensions of Gaussian Type Quadratic Relations Involving Numbers of Solutions of Conditional Equations in Finite Fields, Proceedings of the National Academy of Sciences, 38:981-991, November 1952. 2/49 Vandiver, H. S., A Development of Associative Algebra and an Algebraic Theory of Numbers, I, Math Magazine, 25:233-250, 1952. 2/50 Pearson, Erna H. and H. S. Vandiver, On a New Problem Concerning Trinomial Congruences Involving Rational Integers, Proceedings of the National Academy of Sciences, 39:1278-1285, December 1953. 2/51 Vandiver, H. S., On the Mathematical Work of Dimitry Mirimanoff, L'Enseignement Mathematique, Geneva, Switzerland, 39:169-179, 1952. 2/52 Vandiver, H. S., A Development of Associative Algebra and an Algebraic Theory of Numbers, II, Math Magazine, 27:1-18, 1953. 2/53 Vandiver, H. S., New Types of Trinomial Congruence Criteria Applying to Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 40:248-252, April 1954. 2/54 Vandiver, H. S., The Relation of Some Data Obtained from Rapid Computing Machines to the Theory of Cyclotomic Fields, Proceedings of the National Academy of Sciences, 40:474-480, June 1954. 2/55 Vandiver, H. S., Examination of Methods of Attack on the Second Case of Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 40:732-735, August 1954. 2/56 Nicol, C. A. and H. S. Vandiver, A Von Sterneck Arithmetical Function and Restricted Partitions with Respect to a Modulus, Proceedings of the National Academy of Sciences, 40:825-835, September 1954. 2/57 Vandiver, H. S., On Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 40:1008-1010, October 1954. 2/58 Lehmer, D. H. and Emma Lehmer and H. S. Vandiver, An Application of High-Speed Computing to Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 40:25-33, 1954. 2/59 Nicol, C. A. and H. S. Vandiver, On Generating Functions for Restricted Partitions of Rational Integers, Proceedings of the National Academy of Sciences, 41:37-42, January 1955. 2/60 Vandiver, H. S., Divisibility Problems in Number Theory, Scripta Mathematica, 21:15-19, March 1955. 2/61 Vandiver, H. S., On the Properties of Certain Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 41:651-653, September 1955. 2/62 Vandiver, H. S., Relation of the Theory of Certain Trinomial Equations in a Finite Field to Fermat's Last Theorem, Proceedings of the National Academy of Sciences, 41:770-775, October 1955. 2/63 Vandiver, H. S., On the Divisors of the Second Factor of the Class Number of a Cyclotomic Field, Proceedings of the National academy of Sciences, 41:780-783, October 1955. 2/64 Vandiver, H. S., On Cyclotomic Relations and Trinomial Equations in a Finite Field, Proceedings of the National Academy of Sciences, 41:775-780, October 1955. 2/65 Nicol, C. A. and J. L. Selfriedge and H. S. Vandiver, Proof of Fermat's Last Theorem for All Prime Exponents Less Than 4002, Proceedings of the National Academy of Sciences, 41:970-973, November 1955. 2/66 Vandiver, H. S., Is There an Infinity of Regular Primes? Scripta Mathematica, 21:306-309, December 1955. 2/67 Vandiver, H. S. and M. W. Weaver, A Development of Associative Algebra and an Algebraic Theory of Numbers, III, Mathematics Magazine, 29: 135-151, January-February 1956. 2/68 Nicol, C. A. and J. L. Selfridge and H. S. Vandiver, On Diophantine Equations Which Have No Solutions, Proceedings of the National Academy of Sciences, 42:264-266, May 1956. 2/69 Vandiver, H. S., Diophantine Equations in Certain Rings, Proceedings of the National Academy of Sciences, 42:656-665, September 1956. 2/70 Vandiver, H. S. and M. W. Weaver, A Development of Associative Algebra and an Algebraic Theory of Numbers, IV, Mathematics Magazine, 30:1-8, 1956. 2/71 Lehmer, Emma and H. S. Vandiver, On the Computation of the Number of Solutions of Certain Trinoial Congruences, Journal of the Association for Computing Machinery, 4:505-510, October 1957. 2/72 Vandiver, H. S., The Rapid Computing Machine as an Instrument in the Discovery of New Relations in the Theory of Numbers, Proceedings of the National Academy of Sciences, 44:459-464, May 1958. 2/73 Nicol, C. A. and H. S. Vandiver, Supplement to a Paper Entitled 'A Von Sterneck Arithmetical Function and Restricted Partitions with Respect to a Modulus, Proceedings of the National Academy of Sciences, 44:917-918, September 1958. 2/74 Vandiver, H. S., Some Aspects of the Fermat Problem (Fourth Paper), Proceedings of the National Academy of Sciences, 49:601-608, May 1963. 2/75 Vandiver, H. S. and M. W. Weaver, Introduction to Arithmetic Factorization and Congruences from the Standpoint of Abstract Algebra, American Mathematical Monthly, 65:1-53, October 1958. (Part II, no. 7 of the Herbert Ellsworth Slaught Memorial Papers). 2/76 Vandiver, H. S., On Distribution Problems Involving the Numbers of Solutions of Certain Trinomial Congruences, Proceedings of the National Academy of Sciences, 45:1635-1641, November 1959. 2/77 Vandiver, H. S., On Conditional Fractional Equations in a Field, Involving One Unknown, Mathematics Magazine, 32:173-173, 1959. 2/78 Vandiver, H. S., On the Use of the Equivalence Symbol and Parentheses Symbols in Associative Distributive Algebra, Mathematics Magazine, 32:13-20, January 1960. 2/79 Vandiver, H. S., On the Desirability of Publishing Classified Bibliographies of the Mathematics Literature, American Mathematical Monthly, 67:47-50, January 1960. 2/80 Vandiver, H. S., On the Use of Abstract Algebra as a Method for Obtaining Results Involving Rational Integers Only and the Reverse of this Procedure, Proceedings of the National Academy of Sciences, 46:545-554, April 1960. 2/81 Vandiver, H. S., Some Aspects of the Fermat Problem (First Paper), Proceedings of the National Academy of Sciences, 47:202-209, February 1961. 2/82 Vandiver, H. S., Some Aspects of the Fermat Problem (Second Paper), Proceedings of the National Academy of Sciences, 47:585-590, April 1961. 2/83 Vandiver, H. S., Some Aspects of the Fermat Problem (Third Paper), Proceedings of the National Academy of Sciences, 47:1831-1838, November 1961. 2/84 Vandiver, H. S., On Developments in an Arithmetic Theory of the Bernoulli and Allied Numbers, Scripta Mathematics, 25:273-303, 1961. 2/85 Vandiver, H. S., Some Aspects of the Fermat Problem (Fourth Paper), Proceedings of the National Academy of Sciences, 49:601-608, May 1963. 2/86 Vandiver, H. 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