## Task B-3.5.

Solve the equation $a^{2}+b^{2}+50=8a+12b$ in the set of integers.
## Solution.

If we write the given equation in the form $a^{2}-8 a+16+b^{2}-12 b+36=2$, we see that it is equivalent to the equation $(a-4)^{2}+(b-6)^{2}=2$.

This equality will be true in the set of integers only if

$$
a-4= \pm 1 \quad \text { and } \quad b-6= \pm 1
$$

Thus, $a=3$ or $a=5$, and $b=5$ or $b=7$. The solutions are

$$
(a, b) \in\{(3,5),(3,7),(5,5),(5,7)\}
$$