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Proceedings of the American Mathematical Society

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

 

 

Partitions with equal products. II


Author: John B. Kelly
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
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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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DOI: https://doi.org/10.1090/S0002-9939-1989-0984800-0
Keywords: Partition, elliptic curve, torsion group
Article copyright: © Copyright 1989 American Mathematical Society