Find all $\displaystyle a,b\in\mathbb{Z}^+$ such that (ab²+b+7)|(a²b+a+b)
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Originally Posted by streethot Find all $\displaystyle a,b\in\mathbb{Z}^+$ such that (ab²+b+7)|(a²b+a+b) Polynomial (in a) division: a^2b + a + b | ab^2 + b + 7 ____________|____________ a^b + a +7a/b| a/b ------------- |---------------------- b - 7a/b | So it must be b - 7a/b = 0 ==> b^2 = 7a ==> a = 7k^2, b = 7k, k an integer. Tonio
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