Question: need state and steps Let a and b be positive integers. Prove that if ma2 + nb2 = god(a, b) for some integers m and

need state and steps

Let a and b be positive integers. Prove that if ma2 + nb2 = god(a, b) for some integers m and n then god(a, b) = 1. (Hint: In a direct proof or a proof by contradiction, first show that god(a, b)2 | god(a, b). Then using god(a, b)2 | god(a, b) show that god(a, b) = 1 holds.)

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