Modular Arithmetichard
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Hensel's Lemma allows lifting solutions of f(x)0(modp)f(x) \equiv 0 \pmod p to xa(modpk)x \equiv a \pmod{p^k}. For f(x)=x27f(x) = x^2 - 7, which x(mod3)x \pmod 3 can be lifted to x(mod9)x \pmod 9?