Question

Prove that if r!= (-1) (mod p), then (p-r-1)!= -1 (mod p). lint: Observe that p-i-i (mod p) and write out Wilson's theorem.)

Answer 1

To prove the statement, we can use Wilson's theorem.

Step-by-step explanation:

In order to prove the given statement, we can use Wilson's theorem. Wilson's theorem states that if p is a prime number, then (p-1)! ≡ -1 (mod p).

Given that r! ≠ -1 (mod p), we know that r! is not congruent to -1 modulo p. Since p is prime, we can use Wilson's theorem to conclude that (p-r-1)! is congruent to -1 modulo p.

Therefore, if r! ≠ -1 (mod p), then (p-r-1)! is congruent to -1 modulo p.