1. Given that x is a positive integer prove that f(x) = x2 + x + 1 will never divide by 5.
2. Consider the expression xx + 1, where x be a positive integer.
It can be verified that x = 7 is the least value for which xx + 1 divides by 23.
Given that n is a positive integer, find the least value of x for which xx + 1 is divisible by 2n.