1. ## Congruences and fields

Let p be a prime number. Use the fact that Zp is a field to prove that (p-1)! is congruent to -1(mod p).

Hint: Pair elements of Zp with their multiplicative inverses.

2. Originally Posted by meggnog
Let p be a prime number. Use the fact that Zp is a field to prove that (p-1)! is congruent to -1(mod p).

Hint: Pair elements of Zp with their multiplicative inverses.

That is a huge hint: what've you done so far?

Tonio