This problem consists of four parts.1. Show that for any nonzero integers m,n, and prime p, we have vp(mn)=vp(m)+vp(n).2. Show that if an off prime p, a positive integer k and integers a,b satisfy p∤’p∣a−b and p∤k, then vp(ak−bk)=vp(a−b).3. Show that if p is an off prime with p∣a−b and p∤a,b, then vp(ap−bp)=vp(a−b)+1).4. Show that if an odd prime p, a positive integer k and integers a,b satisfy p∤a,b’p∣a−b, then vp(ak−bk)=vp(a−b). Proposed by LTE.