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 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Partitions with equal products. II
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by John B. Kelly
Proc. Amer. Math. Soc. 107 (1989), 887-893
DOI: https://doi.org/10.1090/S0002-9939-1989-0984800-0

Abstract:

The following theorem is proved: Let $k \geq 3$ and $r$ be positive integers. There exist infinitely many integers having $r$ partitions into $k$ parts such that the products of the integers in each partition are equal. Moreover, these partitions are mutually disjoint, i.e., no integer occurs in more than one of them. Of some additional interest is a lemma stating that a certain class of elliptic curves has positive rank over ${\mathbf {Q}}$.
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Bibliographic Information
  • © Copyright 1989 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 107 (1989), 887-893
  • MSC: Primary 11P57
  • DOI: https://doi.org/10.1090/S0002-9939-1989-0984800-0
  • MathSciNet review: 984800