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Perfect Powers that are Sums of Squares of an Arithmetic Progression

Published 24 Sep 2018 in math.NT | (1809.09167v2)

Abstract: In this paper, we determine all primitive solutions to the equation $(x+r)2 +(x+2r)2 +\cdots +(x+dr)2 = yn$ for $2\leq d\leq 10$ and for $1\leq r\leq 104$. We make use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

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