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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality 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

Abstract:

This paper presents a simple proof that every nonnegative integer is the sum of $m + 2$ polygonal numbers of order $m + 2$.
References
    A. Cauchy, Démonstration du théorème général de Fermat sur les nombres polygones, Mém. Sci. Math. Phys. Inst. France (1) 14 (1813-15), 177-220 = Oeuvres (2), vol. 6, 320-353.
  • L. E. Dickson, All positive integers are sums of values of a quadratic function of $x$, Bull. Amer. Math. Soc. 33 (1927), no. 6, 713–720. MR 1561454, DOI 10.1090/S0002-9904-1927-04464-0
  • P. Fermat, quoted in T. L. Heath, Diophantus of Alexandria, Dover, New York, 1964, p. 188.
  • Carl Friedrich Gauss, Disquisitiones arithmeticae, Yale University Press, New Haven, Conn.-London, 1966. Translated into English by Arthur A. Clarke, S. J. MR 0197380
  • J. L. Lagrange, DĂ©monstration d’un thĂ©orème d’arithmĂ©tique, Nouveaux MĂ©moires de l’Acad. Royale des Sci. et Belles-L. de Berlin, 1770, pp. 123-133 = Oeuvres, vol. 3, pp. 189-201. A.-M. Legendre, ThĂ©orie des nombres, 3rd ed., vol. 2, 1830, pp. 331-356.
  • 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: https://doi.org/10.1090/S0002-9939-1987-0866422-3
  • MathSciNet review: 866422