Help! Please!
Prove that if n is an element of Z(the integers) and log2n is rational, then log2n is an integer.
(We can assume that n>1).
Suppose that where is a positive rational number. This means . Now the fundamental theorem of arithmetic allows us to factorize , the thing is that all factors much be 's because the LHS is made out of two, thus, . This means, . Thus, which means which tells us that is an integer.