2015/010)If p is prime, then what is the remainder of (p - 2)! / p

say (p - 2)! ≡ x (mod p)
multiply by (p-1)

(p-1)! = x(p-1) mod p

so -1 = x (p-1) mod p as (p-1) ! = - 1 mod p

p-1 = -1 mod d

so -1 = x (-1) mod p = - x mod p

so -x mod p = - 1

or x mod p = 1

 so  remainder of (p - 2)! / p is 1