Salajan's conjecture on discriminating terms in an exponential sequence

2015/04/22 by Pieter Moree, Ana Zumalacárregui · 1 citation
Mathematics · #math.NT

paper · pdf

published as J. Number Theory 160 (2016), 646--665 · 18 pages

arxiv created 2015/04/22 · arxiv updated 2020/08/27

Abstract

Given a sequence of distinct positive integers v₁,v₂,… and any positive integer n, the discriminator D_v(n) is defined as the smallest positive integer m such v₁,…,v_n are pairwise incongruent modulo m. We consider the discriminator for the sequence u₁,u₂,…, where u_j equals the absolute value of ((-3)^j-5)/4, that is u_j=(3^j-5(-1)^j)/4. We prove a 2012 conjecture of Sabin Salajan characterizing the discriminator of the sequence u₁,u₂,….

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• Browkin's discriminator conjecture

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