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Question

How many ordered pairs of positive integers (x,y) satisfy the equation xy+yx+2006xy2006x2006y2006=0?
(correct answer + 3, wrong answer 0)

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Solution

xy+yx+2006xy2006x2006y2006=0
(x+y+2006)(xy2006)=0
(xy2006)=0 (x+y+2006>0)
xy=2006=17×59×2
Thus the solutions are
(1,2006),(2006,1),(2,1003),(1003,2),(34,59),(59,34),(17,118),(118,17)

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