8. (Section 1.3 #10) Let p be an integer other than 0, ±1. Prove
p is...
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8. (Section 1.3 #10) Let p be an integer other than 0, ±1. Provep is prime if and only if for all a 2 Z either (a, p) = 1 OR p | a. 9. (Section 1.3 #16) Prove that (a, b) = 1 if and only if there isno prime p such that p | a AND p | b.
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8 a be an integer which is not divisible by a and p is prime The only common divisors of a are 1 and 1and the only divisors of p are 1 1 p p Therefore a p 1 Since this argument works for every integer
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