175. A divisor of its palindrome. In what base does 792 divide 297?

Note: The original problem statement is in Russian, but the provided translation is in English as requested.
175. In any number system with base $B \geqslant 10$ the following inequalities hold:

$$
2(297)<2(300)=600<792<800=4(200)<4(297)
$$

Therefore, $792=3(297)$, so $7 B^{2}+9 B+2=3\left(2 B^{2}+9 B+7\right)$, or $B^{2}-18 B-19=0$. Discarding the negative root of this quadratic equation, we get $B=19$.

[D. L. Silverman, M. M., 38, 124 (March 1965).]