Solve Hard GCD Problems: Prove d=d1d2 with d1|a and d2|b

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lordy12

1. If d|ab and gcd(a,b)=1, prove that d=d1d2 where d1|a and d2|b and gcd(d1,d2) = 1

Homework Equations

3. Let d1 = gcd(d,a). Thats all I know

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Write down prime decompositions for a, b, and ab, and see if that helps you out.