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Math Help - Division problem

  1. #1
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    Division problem

    Find all a,b\in\mathbb{Z}^+ such that (ab+b+7)|(ab+a+b)
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  2. #2
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    Quote Originally Posted by streethot View Post
    Find all a,b\in\mathbb{Z}^+ such that (ab+b+7)|(ab+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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