Question: Prove the theorem with step-by-step answers and explanations: Theorem. Let a and b be integers. Then a and b are relatively prime if and only

Prove the theorem with step-by-step answers and explanations: Theorem. Let ( a ) and ( b ) be integers. Then ( a ) and ( b ) are relatively prime if and only if there exist intege

Theorem. Let a and b be integers. Then a and b are relatively prime if and only if there exist integers x and y so that ax + by 1. The next theorem is a generalization of this theorem. Theorem 1. For any integers a and b that are not both 0, there exist integers x and y such that ax+by = gcd (a, b).

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