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 July 8th, 2019, 11:42 PM #1 Senior Member   Joined: Dec 2015 From: somewhere Posts: 636 Thanks: 91 Solve for integers Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy$, where $x,y$ are integers. Last edited by skipjack; July 9th, 2019 at 02:22 AM.
July 9th, 2019, 01:36 AM   #2
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Quote:
 Originally Posted by idontknow Find all pairs $\displaystyle (x,y)$ such that $\displaystyle x+y=xy \;$ , where x,y integers .
Solving for y:
$\displaystyle y = \dfrac{x}{x - 1}$

If y is to be an integer that means that x must be a multiple of x - 1. The only possibilities are x = 0, giving y = 0 and x = 2, giving y = 2.

So the solution set is (x, y) = {(0, 0), (2, 2)}.

-Dan

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