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Two variable diophantine equation

Source: Costa Rica National Olympiad, Final Round, Problem 4

October 14, 2011
inequalitiesnumber theory unsolvednumber theory

Problem Statement

Find all integer solutions (a,b)(a,b) of the equation (a+b+3)2+2ab=3ab(a+2)(b+2) (a+b+3)^2 + 2ab = 3ab(a+2)(b+2)
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