I (probably re)invented a very short combinatorial proof of Wilson's theorem that I perennially teach my students. If it occurs in the literature and someone can tell me where first (or even at all), I would like to attribute credit properly.

I actually prove $p! - p(p-1) \equiv 0 \mod p^2$.

$p!$ counts bijective function from ${\Bbb Z}/p$ to ${\Bbb Z}/p$ and ${\Bbb Z}/p \times {\Bbb Z}/p$ acts on these by $f(x)\stackrel{(a,b)}{\rightarrow} f(x-a)+b$. Excluding functions of the form $cx+d, c\not=0$, all orbits have size $p^2$.