Perfect powers in sum of three fifth powers

2020/08/18 by Das, Pranabesh, Dey, Pallab Kanti, Koutsianas, Angelos +1
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2008.07804

Abstract

In this paper we determine the perfect powers that are sums of three fifth powers in an arithmetic progression. More precisely, we completely solve the Diophantine equation (x-d)⁵ + x⁵ + (x + d)⁵ = zⁿ,~n≥ 2, where d,x,z ∈ ℤ and d = 2^a5^b with a,b≥ 0.

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