Suppose we know $p$ and $q$ two prime number, is there a way to find $x$ to satisfy this equation for $x$: given $a$ and $n$ where $n =pq$ find $x$ such that $x^2=a \bmod n$.
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emacs drives me nuts
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2There are some other questions / answers that address this, but none of them are very satisfactory, IMO like https://math.stackexchange.com/a/633174/746312 but maybe it's good enough for you? Basically (assuming $p\neq q$) solve for each prime individually and then use the Chinese Remainder Theorem to combine them. – emacs drives me nuts Sep 08 '22 at 14:24
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thank you sir for your precious time. – sam oldfield 999 Sep 08 '22 at 14:56
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1For square roots modulo a (large) prime, there is the Tonelli-Shanks algorithm. – Jaap Scherphuis Sep 08 '22 at 15:21
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sir, thank you for your precious time I appreciate that. – sam oldfield 999 Sep 14 '22 at 13:46