April 25, 2024Open Access

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

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Abstract

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

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András Bazsó (Thu,) studied this question.

synapsesocial.com/papers/68e6dac2b6db6435876575b4 https://doi.org/https://doi.org/10.48550/arxiv.2404.16535

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