For natural numbers \(x\) and \(y\), let \((x, y)\) denote the greatest common divisor of \(x\) and \(y\). How many pairs of natural numbers \(x\) and \(y\) exist with \(x \leq y\) satisfy the equation \(xy = x + y + (x,y)\)?

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TopNewestThe answer is 3 i.e. (2,3) (2,4) (3,3) I did this by hit and trial method as I had realised that there won't be any pair which will have any number greater than 4 in it. So it took around 2 minutes to solve it

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the answer is 3. take g as gcd and then keep analysing number theoritically what could be the values of g.

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I think answer is 2

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Is answer 3??

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Even I got 3 pairs. \((2,3), (2,4) \) and \((3, 3)\). How did you solve it?

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