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arXiv · 1312.3531

On equal values of power sums of arithmetic progressions

A. Bazsó·D. Kreso·F. Luca·Á. Pintér
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Abstract

In this paper we consider the Diophantine equation \begin{align*}b^k +\left(a+b\right)^k &+ \cdots + \left(a\left(x-1\right) + b\right)^k=\\ &=d^l + \left(c+d\right)^l + \cdots + \left(c\left(y-1\right) + d\right)^l, \end{align*} where $a,b,c,d,k,l$ are given integers. We prove that, under some reasonable assumptions, this equation has only finitely many integer solutions.

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A. Bazsó, D. Kreso, F. Luca, Á. Pintér. 2013-12-12. On equal values of power sums of arithmetic progressions. https://doi.org/10.3336/gm.47.2.02

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