Arithmetic progressions consisting of unlike powers

2005/12/17 by Bruin, N., Gyory, K., Hajdu, L. +1
#11D41 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.math/0512419

Abstract

In this paper we present some new results about unlike powers in arithmetic progression. We prove among other things that for given k≥ 4 and L≥ 3 there are only finitely many arithmetic progressions of the form (x₀^l₀,x₁^l₁,...,x_k-1^l_k-1) with x_i∈\Bbb Z, gcd(x₀,x₁)=1 and 2≤ l_i≤ L for i=0,1,...,k-1. Furthermore, we show that, for L=3, the progression (1,1,...,1) is the only such progression up to sign.

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