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Proceedings of the American Mathematical Society

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



Completion of a Gaussian derivation

Author: John A. Ewell
Journal: Proc. Amer. Math. Soc. 84 (1982), 311-314
MSC: Primary 10J20; Secondary 05A19
MathSciNet review: 637190
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Abstract: The author supplies evaluation of two coefficients of an identity partially derived by Gauss. Several special cases of this identity are then presented, the last of these identities yielding an alternate proof of Ramanujan’s theorem concerning divisibility of certain values of the partition function by the modulus 7.

References [Enhancements On Off] (What's this?)

    G. H. Hardy, Ramanujan, Chelsea, New York, 1959. G. H. Hardy and E. M. Wright, An introduction to the theory of numbers, 4th ed., Clarendon Press, Oxford, 1960.
  • Percy A. MacMahon, Combinatory analysis, Chelsea Publishing Co., New York, 1960. Two volumes (bound as one). MR 0141605

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Keywords: Identities, partition function, triple-product identity
Article copyright: © Copyright 1982 American Mathematical Society