My attempt at a formal proof by induction.
For a number x in the set of natural numbers, prove that there is no value for x such that 2^x mod 3 = 0.
For some number n mod 3 to be equal to 0, 3 must be a number in n's prime factorization.
Assume that 2^x mod 3 != 0.
2^x has a prime...