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

2018/02/21 by Koutsianas, Angelos, Patel, Vandita
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1802.07485

Abstract

We determine primitive solutions to the equation (x-r)² + x² + (x+r)² = yⁿ for 1 ≤ r ≤ 5,000, making use of a factorization argument and the Primitive Divisors Theorem due to Bilu, Hanrot and Voutier.

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