On equal values of products and power sums of consecutive elements in an arithmetic progression
Number Theory
2023-02-17 v1
Abstract
In this paper we study the Diophantine equation \begin{align*} b^k + \left(a+b\right)^k + &\left(2a+b\right)^k + \ldots + \left(a\left(x-1\right) + b\right)^k = \\ &y\left(y+c\right) \left(y+2c\right) \ldots \left(y+ \left(\ell-1\right)c\right), \end{align*} where are given integers under natural conditions. We prove some effective results for special values for and and obtain a general ineffective result based on Bilu-Tichy method.
Cite
@article{arxiv.2302.08400,
title = {On equal values of products and power sums of consecutive elements in an arithmetic progression},
author = {András Bazsó and Dijana Kreso and Florian Luca and Ákos Pintér and Csaba Rakaczki},
journal= {arXiv preprint arXiv:2302.08400},
year = {2023}
}