Who tells thou that among the prime decomposition the p_i's are different from 2?
Instead decompose n>1 as n=2^m*p1^(a1)*...*pk^ak where m>=0
The Euler Phi function counts the number of positive integers less than or equal to n, which are relatively prime to n.
Prove that if n is odd, then , and if n is even, then . I don't really know how to begin.
Here's my attempt to prove the first part, if n is odd, .
Let the prime decomposition of n be .
So,
But it seems like this would work for all n, not just odd n, so my above proof must be wrong.