One number-theoretic result mentioned in the course was Wilson’s Theorem : If p is a prime then (p − 1)! is congruent to −1 mod p . — The purpose of this exercise is to show the reverse implication....

One number-theoretic result mentioned in the course was
Wilson’s


Theorem:
If p is a prime then (p − 1)! is congruent to −1 mod p. — The purpose of this exercise is to show the reverse implication.

Suppose n > 1 is a composite integer ab where a and b are
unequal
integers both greater than 1. Prove that (n − 1)! is congruent to 0 mod n. [Hint: Why are both factors less than n/2?]