Power Values of Divisor Sums

F. Beukers; Florian Luca; F. Oort

doi:10.4169/amer.math.monthly.119.05.373

Power Values of Divisor Sums

F. Beukers, Florian Luca, F. Oort

Afd Mathematisch Instituut

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Research output: Contribution to journal › Article › Academic › peer-review

Abstract

We consider positive integers whose sum of divisors is a perfect power. This problem had already caught the interest of mathematicians from the 17th century like Fermat, Wallis and Frenicle. In this article we study this problem and some variations.We also give an example of a cube, larger than one, whose sum of divisors is again a cube.

Original language	English
Pages (from-to)	373-380
Number of pages	8
Journal	The American mathematical monthly.
Volume	119
Issue number	5
DOIs	https://doi.org/10.4169/amer.math.monthly.119.05.373
Publication status	Published - 2012

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abstract = "We consider positive integers whose sum of divisors is a perfect power. This problem had already caught the interest of mathematicians from the 17th century like Fermat, Wallis and Frenicle. In this article we study this problem and some variations.We also give an example of a cube, larger than one, whose sum of divisors is again a cube.",

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DO - 10.4169/amer.math.monthly.119.05.373

M3 - Article

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SP - 373

EP - 380

JO - The American mathematical monthly.

JF - The American mathematical monthly.

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Power Values of Divisor Sums

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