## Task A-1.2.

Let $a, b, c, d$ be distinct integers such that

$$
(a-2024)(b-2024)(c-2024)(d-2024)=9
$$

Determine $a+b+c+d$.
## Solution.

Since $a, b, c, d$ are distinct integers, then $a-2024, b-2024$, $c-2024$, and $d-2024$ are also distinct integers.

For the product of 4 distinct integer divisors of 9 to equal 9, none of them can be 9 or -9. The remaining divisors of 9 are $-3, -1, 1, 3$.

Since their product is 9, we conclude that these are the values of the factors $a-2024$, $b-2024$, $c-2024$, and $d-2024$.

Therefore,

$$
\begin{aligned}
a+b+c+d & =(a-2024)+(b-2024)+(c-2024)+(d-2024)+4 \cdot 2024 & & 1 \text { point } \\
& =-3-1+1+3+8096=8096 & & 1 \text { point }
\end{aligned}
$$