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$$x^2 \equiv 134 \text{ mod } 197$$ $$x^2 \equiv 134 \text{ mod } 197^2\times 67$$ $$x^2 \equiv 134 \text{ mod } 197^{30}\times2^{10}$$ $$x^2 \equiv 134 \text{ mod } 197\times 23^2$$

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

ʎpoqou
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  • Perhaps with that last line I can deduce that 2 and 3 will also have solutions but the last one will not because there, the 23 causes trouble? – ʎpoqou Apr 13 '19 at 13:10
  • see the answer for this link (https://math.stackexchange.com/questions/335179/quadratic-congruence-with-chinese-remainder-thm). This will guide you! – Chinnapparaj R Apr 13 '19 at 13:15

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