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July 8th, 2019, 11:42 PM   #1
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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.
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July 9th, 2019, 01:36 AM   #2
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Originally Posted by idontknow View Post
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)}.

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