Effective results for polynomial values of (alternating) power sums of arithmetic progressions

2024/04/25 by András Bazsó, Bazsó, András
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2404.16535

openalex publication_date 2024/04/25 · openalex created_date 2024/04/27 · openalex updated_date 2026/07/28

Abstract

We prove effective finiteness results concerning polynomial values of the sums b^k +(a+b)^k + ⋯ + (a(x-1) + b)^k and b^k - (a+b)^k + (2a+b)^k - … + (-1)^x-1 (a(x-1) + b)^k , where a ≠ 0,b, k are given integers with gcd(a,b)=1 and k ≥ 2.

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