Salajan's conjecture on discriminating terms in an exponential sequence

Given a sequence of distinct positive integers v1,v2,…v1,v2,… and any positive integer n  , the discriminator Dv(n)Dv(n) is defined as the smallest positive integer m   such that v1,…,vnv1,…,vn are pairwise incongruent modulo m  . We consider the discriminator for the sequence u1,u2,…u1,u2,… , where ujuj equals the absolute value of ((−3)j−5)/4((−3)j−5)/4, that is uj=(3j−5(−1)j)/4uj=(3j−5(−1)j)/4. We prove a 2012 conjecture of Sabin Salajan characterizing the discriminator of the sequence u1,u2,…u1,u2,… .