# Find all integers a and b such that $2a + 2b = ab$ . [closed]

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

• 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? May 27 '19 at 4:00
• What have you tried? May 27 '19 at 4:03
• Hint: $2(a+b) = ab \iff (a-2)(b-2) = 4$. May 27 '19 at 4:04

\begin{align} 2a+2b &= ab \\ ab-2a-2b &= 0 \\ a(b-2)-2b &= 0 \\ a(b-2)-2b+4 &= 0+4 = 4 \\ a(b-2)-2(b-2) &= 4 \\ (a-2)(b-2) &= 4 \end{align}