If gcd(a,n) = 1 and gcd(a-1,n) = 1 then prove that
1 + a + a^2 + a^3 + ... + a^(phi-1) = 0 (mod n)
Where phi = phi(n) is the Euler phi/totient function.
= means "is congruent to"
I can prove this if n is a prime number, but I need the proof for any n > 1.
a and n are integers, of course.