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.
No takes yet. Share an insight, caveat, or question.
András Bazsó (2024) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: