Homework Statement
a > 1, k > 0. Show that k divides \phi(a^k - 1), where \phi is Euler's totient function (Hint: use some group theory).
Homework Equations
If n = p_1^{a_1}p_2^{a_2}...p_m^{a_m}, then \phi(n) = n(1 - 1/p_1)(1 - 1/p_2)...(1 - 1/p_m)
The Attempt at a Solution
I guess...