Let a,b be any relatively prime positive numbers. (The case b = 1 is allowed). We...

Let a,b be any relatively prime positive numbers. (The case b = 1 is allowed). We have the rational number a/b. Without appealing to anything but Euclid’s lemma (no use of ε(p, m)) show that if p is prime then p does not equal (a/b)^2. That is √p is irrational. Hint: if p = (a/b)^2 then we have p(b^2) = a^2. Derive p|b and then show p|a which is a contradiction.

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Colby Messinger answered 1 year ago

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