How do I prove: Let p be a prime number. Show that for any integer a the greatest common divisor of p and a is either p (if p|a) or is 1 (if p does not divide a).

Let n be a positive integer. Write the digits of n in decreasing order, then write the digits in decreasing order, then subtract. Prove that the answer is always divisible by 9.

(1) Let p be a prime number. Show that for any integer a the greatest common divisor of p and a is either p (if pla) or is 1 (if p does not divide a).

Prove that if an integer m has the same parity as an integer n, 5m + 7n is even. Discrete math