Prove that (kk) is periodic modulo 3 and find its period.
A function f(x) is periodic if there exists some minimum n such that f(x+n) = f(x) for all x in the domain of f. For instance, you all know f(x) = sin x = f(x+2pi) for all real x.
For the homework problem as stated, you want to prove that f(k) = k^k mod 3 is periodic for all integers. Find the minimum n as stated in the definition, and prove this holds for all k. For this problem, I have decided to limit this to allnatural numbers k, since 0^0 throws off the periodic pattern of the function.