3. Let $\{x, y, z, t\}=\{12,14,37,65\}$. Determine the numbers $x, y, z, t$ if

$$
x y - x z + y t = 182
$$
Solution. A direct check (24 possibilities) yields the only solution $x=12, y=37, z=65, t=14$. We leave it to the reader to simplify the procedure, for example, by considering remainders upon division by 2 and 3 of the number 182 and the products of any two of the numbers 12, 14, 37, and 65.