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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A short proof of Cauchy’s polygonal number theorem
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by Melvyn B. Nathanson PDF
Proc. Amer. Math. Soc. 99 (1987), 22-24 Request permission


This paper presents a simple proof that every nonnegative integer is the sum of $m + 2$ polygonal numbers of order $m + 2$.
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  • P. Fermat, quoted in T. L. Heath, Diophantus of Alexandria, Dover, New York, 1964, p. 188.
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  • Gordon Pall, Large Positive Integers are Sums of Four or Five Values of a Quadratic Function, Amer. J. Math. 54 (1932), no. 1, 66–78. MR 1506873, DOI 10.2307/2371077
  • T. Pepin, DĂ©monstration du thĂ©orème de Fermat sur les nombres polygones, Atti Accad. Pont. Nuovi Lincei 46 (1892-93), 119-131. J. V Uspensky and M. A. Heaslet, Elementary number theory, McGraw-Hill, New York and London, 1939.
  • AndrĂ© Weil, Number theory, Birkhäuser Boston, Inc., Boston, MA, 1984. An approach through history; From Hammurapi to Legendre. MR 734177, DOI 10.1007/978-0-8176-4571-7
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Additional Information
  • © Copyright 1987 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 99 (1987), 22-24
  • MSC: Primary 11B83
  • DOI:
  • MathSciNet review: 866422