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 $$ (x-d)^5 + x^5 + (x + d)^5 = z^n,~ngeq 2, $$ where $d,x,z in mathbb{Z}$ and $d = 2^a5^b$ with $a,bgeq 0$.
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