Exercises

Exercises

E: Prove, by considering suitable actions, the following facts:

• " n Î N^*: å_{d | n} f(d)=n.
• " prime p: (p-1)! º-1 (p) (Wilson).
• " z Î Z,p prime, n Î N^*: z^(pn) ºz^(pn-1) (pⁿ).
• " z Î Z,n Î N^* such that gcd (z,n)=1: z ^f(n) º1 (n) (Euler).

Exercises