Question 1209235
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Find the number of ordered pairs (m,n) of integers that satisfy
mn = 3m + 3n + 17.
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Transform the given equation this way

    mn - 3m - 3n + 9 = 26,

    (n-3)*(m-3) = 26.


So, n-3 and m-3 are divisors of 26.


There are 4 different decompositions of 26 into the product of positive integer numbers

    8 = 1*26 = 2*13 = 13*2 = 26*1


It gives 4 different pairs (m,n).         // Since the problem does not ask to find them,
                                             I will not find them.



There are 4 different decompositions of 26 into the product of negative integer numbers

    26 = (-1)*(-26) = (-2)*(-13) = (-13)*(-2) = (-26)*(-1).


It gives 4 other different pairs (m,n).   // Since the problem does not ask to find them,
                                             I will not find them.


In all, there are 4+4 = 8 different pairs of integer numbers, satisfying the given equation.
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Solved.