§ Wilson's theorem
- We get (mod ) implies is a square root of -1.
- It turns that this is because from Wilson's theorem, .
- Pick . Then in the calculation of , we can pair off with , with and so on.
- So we get .
- This means that .
- The condition is even is the same as saying that is congruent to mod , or that is congruent to mod .
- It's really nice to be able to see where this condition comes from!