Further results on the distinctness of binary sequences derived from primitive sequences modulo square-free odd integers

This paper studies the distinctness of primitive sequences over Z/(M) modulo 2, where M is an odd integer that is composite and square-free, and Z/(M) is the integer residue ring modulo M. A new sufficient condition is given for ensuring that primitive sequences generated by a primitive polynomial f(x) over Z/(M) are pairwise distinct modulo 2. Such result improves a recent result obtained in our previous paper [27] and consequently the set of primitive sequences over Z/(M) that can be proven to be distinct modulo 2 is greatly enlarged