Talk:Wilson's Theorem/Corollary 2

Generalization?
The statement of Wilson's Theorem is:
 * $\paren {p - 1}! \equiv -1 \pmod p$ for primes $p$

How does one recover Wilson's Theorem from this 'generalization'?

For reference if we plug in $n = p - 1$ we have:
 * $a_0 = p - 1, \mu = 0$

hence the theorem asserts that:
 * $\dfrac {\paren {p - 1}!} {p^0} \equiv \paren {-1}^0 \paren {p - 1}! \pmod p$

which is simply
 * $\paren {p - 1}! \equiv \paren {p - 1}! \pmod p$

It could technically be called a Corollary. --RandomUndergrad (talk) 16:31, 8 July 2020 (UTC)


 * Makes sense. Haven't a clue where I got this from now, it was from the early days when we hadn't started citing our source works. I'll rename it. --prime mover (talk) 17:45, 8 July 2020 (UTC)