$$x^2 \equiv 134 \text{ mod } 197$$ $$x^2 \equiv 134 \text{ mod } 197^2\times 67$$ $$x^2 \equiv 134 \text{ mod } 197^{30}\times2^{10}$$ $$x^2 \equiv 134 \text{ mod } 197\times 23^2$$
The firs one has a solution as the Legendre symbol gives 1, but I never got around understanding the other ones.
I notice that $134=2\times67$ but I am not quite sure how to use that for the other parts