On equal values of power sums of arithmetic progressions

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.

arXiv commentThis version differs slightly from the published version in its exposition

Cited by in corpus (4)

• Functional composition of polynomials: indecomposability, Diophantine equations and lacunary polynomials
• On the coefficients of power sums of arithmetic progressions
• Diophantine equations and the monodromy groups
• 30 years of collaboration