- #1
PsychonautQQ
- 784
- 10
Homework Statement
In proving Fermats Theorm, I got confused trying to follow one of the steps.
Theorm: If p is prime, then:
a^p~a (mod p).
part of proof:
multiply all the nonzero elements in Z_p by a to obtain
[a][1],[a][2],...,[a][p-1].
These are all distinct elements and none equal [0], so they must be the set of all nonzero elements [1],[2],...,[p-1] in some order. In particular, the products are the same and we obtain
([a]^(p-1))([1],[2],...,[p-1]) = ([1],[2],...,[p-1])
That fact that those last parts equal each other is confusing me, help?