Prove the following statements:(a) If gcd(a, n) = 1, then the integersform a complete set...

Prove the following statements:

(a) If gcd(a, n) = 1, then the integers

form a complete set of residues modulo n for any c.

(b) Any n consecutive integers form a complete set of residues modulo n.

[Hint: Use part (a).]

(c) The product of any set of n consecutive integers is divisible by n.