Salajan's conjecture on discriminating terms in an exponential sequence

Abstract

Given a sequence of distinct positive integers $v_1,v_2,\ldots$ and any positive integer $n$, the discriminator $D_v(n)$ is defined as the smallest positive integer $m$ such $v_1,\ldots,v_n$ are pairwise incongruent modulo $m$. We consider the discriminator for the sequence $u_1,u_2,\ldots$, 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 $u_1,u_2,\ldots$.