Find the smallest positive integer x where 149|(x^2-69^3) $$
\text{Find the smallest positive integer x where 149|}\left( \text{x}^2-69^3 \right) 
$$
I almost do not spot any clue about this question.
It is from PUMaC-CHINA, 2019.8.17

This follows the comment by  J. W. Tanner and the answer by sirous.
All congruences are mod $149$.
We have $x^2-69^3 \equiv x^2+36 =x^2+6^2 \equiv (x-6j)(x+6j)$, if $j^2\equiv -1$.
Write $149 = 7^2 + 10^2$. Then $10j \equiv 7$ and so $j\equiv 105$.
Thus $x^2-69^3 \equiv (x-34)(x+34)$ and so $34$ is the smallest positive solution.
