On equal values of products and power sums of consecutive elements in an arithmetic progression

2023/02/16 by András Bazsó, Bazsó, András, Dijana Kreso +7
Mathematics · #11B68 #11D41 #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2302.08400

openalex publication_date 2023/02/16 · openalex created_date 2023/02/18 · openalex updated_date 2026/08/01

Abstract

In this paper we study the Diophantine equation b^k + (a+b)^k + amp;(2a+b)^k + … + (a(x-1) + b)^k =
amp;y(y+c) (y+2c) … (y+ (ℓ-1)c), where a,b,c,k,ℓ are given integers under natural conditions. We prove some effective results for special values for c,k and ℓ and obtain a general ineffective result based on Bilu-Tichy method.

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