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Find all integers $a$ and $b$ such that $2a + 2b = ab$.

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closed as off-topic by Cameron Williams, Martin R, Eevee Trainer, John Omielan, YuiTo Cheng May 27 at 6:29

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  • 1
    $\begingroup$ Welcome to MSE. What have you tried? Are you stuck on some concept? Please show your effort and give more details. Is this a homework problem? What level? $\endgroup$ – Andrei May 27 at 4:00
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    $\begingroup$ What have you tried? $\endgroup$ – El Ectric May 27 at 4:03
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    $\begingroup$ Hint: $2(a+b) = ab \iff (a-2)(b-2) = 4$. $\endgroup$ – achille hui May 27 at 4:04
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$$\begin{align} 2a+2b &= ab \\ ab-2a-2b &= 0 \\ a(b-2)-2b &= 0 \\ a(b-2)-2(b-2) &= (-2)(-2) = 4 \\ (a-2)(b-2) &= 4 \end{align}$$

Can you take it from here?

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