Distribution properties of compressing sequences derived from primitive sequences modulo odd prime powers

Let a and b be primitive sequences over Z/(p^e) with odd prime p and e ≥ 2. For certain compressing maps, we consider the distribution properties of compressing sequences of a and b, and prove that a = b if the compressing sequences are equal at the times t such that α(t) = k, where α is a sequence related to a. We also discuss the s-uniform distribution property of compressing sequences. For some compressing maps, we obtain that there exist different primitive sequences such that the compressing sequences are s-uniform. We also discuss that for how many elements s, compressing sequences of different primitive sequences can be s-uniform.