[ equations in integers ]

Solve in integers the equations a) $1 / a+1 / b=1 / 7 ;$ b) $1 / a+1 / b=1 / 25$.
a) Let's write the equation in the form $(a-7)(b-7)=49$. Since $a \neq 0$, then $a-7$ is one of the numbers $-49,-1,1,7,49$. Accordingly, $b-7$ equals $-1,-49,49,7,1$.

## Otvet

a) $\{6,-42\},\{56,8\},(14,14)$.

b) $\{24,-600\},\{20,-100\},\{650,26\},\{150,30\},(50,50)$.