Task A-1.1. (10 points)

Determine all pairs $(a, b)$ of integers such that $a(a-b)=b$.
## First solution.

Let's write the equation in the form $a^{2}=b(a+1)$.

The number $a+1$ is relatively prime to $a$, and it must be a divisor of $a^{2}$.

4 points

Therefore, it must be $a+1=1$ or $a+1=-1$. 3 points

In the first case, $a=0$ and $b=0$, and in the second case, $a=-2$ and $b=-4$.