1 5 + 2 5 + . . . + n 5 1^5+2^5+...+n^5

Find the smallest positive integer n > 1 n>1 , such that k = 1 n k 5 \sum_{k=1}^n k^5 is a perfect square.


The answer is 13.

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1 solution

Giorgos K.
Feb 23, 2018

Mathematica

n=2;While[!IntegerQ[Sqrt[Sum[k^5,{k,n++}]]]];n-1

13

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