Question

Suppose a,b,c belong to Z and gcd(b,c) = 1 . Prove that if b/(ac), then b/a.

Suppose a,b,c belong to Z and gcd(b,c) = 1 . Prove that if b/(ac), then b/a.

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Answer #1

Proof:

Since  ,  there exist integers   and   such that   .

Multiply both side by   we get

Since   and   we have

i.e

i.e  

Hence ,  proved

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