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Let a, b be integers with not both 0. Prove that hcf(a, b) is the smallest...

Let a, b be integers with not both 0. Prove that hcf(a, b) is the smallest positive integer m of the form ra + sb where r and s are integers.
Hint: Prove hcf(a, b) | m and then use the minimality condition to prove that m | hcf(a, b).

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