- #1
mahler1
- 222
- 0
Homework Statement .
This is an exercise I've taken from Rotman's introductory textbook about groups.
Prove Wilson's theorem: If ##p## is a prime, then ##(p-1)!=-1 \text{ mod } p##. He gives the following hint: The nonzero elements of ##\mathbb Z_p## form a multiplicative group. The attempt at a solution.
I couldn't make use of the hint, until now, all I've deduced is: since ##p-1=-1 \text{ mod } p##, then to prove Wilson's theorem would be equivalent to prove that ##(p-1)!=p-1 \text{ mod } p##. Could anyone guide me on how could I use the hint?
This is an exercise I've taken from Rotman's introductory textbook about groups.
Prove Wilson's theorem: If ##p## is a prime, then ##(p-1)!=-1 \text{ mod } p##. He gives the following hint: The nonzero elements of ##\mathbb Z_p## form a multiplicative group. The attempt at a solution.
I couldn't make use of the hint, until now, all I've deduced is: since ##p-1=-1 \text{ mod } p##, then to prove Wilson's theorem would be equivalent to prove that ##(p-1)!=p-1 \text{ mod } p##. Could anyone guide me on how could I use the hint?