Perfect powers that are sums of squares in a three term arithmetic progression

Abstract

We determine primitive solutions to the equation $(x-r{)}^2+x^2+(x+r{)}^2=y^n$ for $1\le r\le 5,000$, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

6 pages