(a) 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?] = p? (b)...

Extracted text: (a) 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?] = p? (b) The preceding part of the problem proves the reverse implication unless n = where p is a prime. Prove that if p > 2 is prime then (p2 – 1)! is congruent to 0 mod p?, and find k E {0,1, 2, 3} such that (22 – 1)! is congruent to k mod 4.