Perfect powers that are sums of squares of an arithmetic progression

We determine all nontrivial integer solutions to the equation (x+r)2+(x+2r)2+⋯+(x+dr)2=yn for 2≤d≤10 and 1≤r≤104 with gcd (x, y) = 1. We make use of a factorization argument and the primitive divisors theorem due to Bilu, Hanrot and Voutier