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arXiv · 2404.16535

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

András Bazsó
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Abstract

We prove effective finiteness results concerning polynomial values of the sums $$ b^k +\left(a+b\right)^k + \cdots + \left(a\left(x-1\right) + b\right)^k $$ and $$ b^k - \left(a+b\right)^k + \left(2a+b\right)^k - \ldots + (-1)^{x-1} \left(a\left(x-1\right) + b\right)^k , $$ where $a \neq 0,b, k$ are given integers with $\gcd(a,b)=1$ and $k \geq 2$.

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András Bazsó. 2024-04-25. Effective results for polynomial values of (alternating) power sums of arithmetic progressions. https://arxiv.org/abs/2404.16535

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