Asian Research Journal of Mathematics

The Product-to-sum Expressing with a Divisor Function σ3(n)

Aeran Kim *

A Private Mathematics Academy, 1599-6-bungi, Keumam-2-dong, Deokjin-gu, Jeonju-si, Jeollabuk-do, 561-806, South Korea.

*Author to whom correspondence should be addressed.

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Abstract

A formula expressing an in nite product as an infinite sum is called a product-to-sum identity. In this paper we try to consider a special product-to-sum as

 

and so for integers r, u, a, b, c, x, y and z we deduce all solutions of (r, u, a, b, c, x, y, z) with r ≥ 0.

Keywords: Divisor functions, infinite product sums, product-to-sum

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