Questions tagged [hensels-lemma]

For questions regarding Hensel's lifting lemma in modular arithmetic and its generalization to commutative rings.

Hensel's Lemma. If a polynomial equation has a simple root modulo a prime number $p$, then this root corresponds to a unique root of the same equation modulo any higher power of $p$, which can be found by iteratively "lifting" the solution modulo successive powers of $p$.

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Given $a^2 \equiv n\pmod q$ find $b$ such that $b^2 \equiv n\pmod {q^2}$

Given $a^2 \equiv n\pmod q$ find $b$ such that $b^2 \equiv n\pmod {q^2}$ $a,n,q$ are given. How to find $b$? I know I am supposed to use Hensel's lemma and "lifting" $q$, I just don't know how to do it.
Ilya Gazman
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