Let be a non trivial subgroup and . Prove that

**Solution**

It is enough to prove it for the case since we can then reduce it by using the fact that

We have that for any integers and . But by Bezout’s lemma we can find such that

and hence .

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# gcd and subgroup

It is enough to prove it for the case since we can then reduce it by using the fact that
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Let be a non trivial subgroup and . Prove that

**Solution**

We have that for any integers and . But by Bezout’s lemma we can find such that

and hence .