A new result on the distinctness of primitive sequences over [formula omitted] modulo 2

Abstract

Let Z / ( p q ) be the integer residue ring modulo pq with odd prime numbers p and q. This paper studies the distinctness problem of modulo 2 reductions of two primitive sequences over Z / ( p q ) , which has been studied by H.J. Chen and W.F. Qi in 2009. First, it is shown that almost every element in Z / ( p q ) occurs in a primitive sequence of order n > 2 over Z / ( p q ) . Then based on this element distribution property of primitive sequences over Z / ( p q ) , previous results are greatly improved and the set of primitive sequences over Z / ( p q ) that are known to be distinct modulo 2 is further enlarged.