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Math Help - Hensel's lemma

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    Hensel's lemma

    My question is if Hensel's lemma is an if and only if. THis is for polynomial congruences. For instance, if there are no solutions to  x^2=a(mod p) , do I get to conclude that there are no solutions to x^2=a(mod p^2), and so on?
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    Quote Originally Posted by Chris11 View Post
    My question is if Hensel's lemma is an if and only if. THis is for polynomial congruences. For instance, if there are no solutions to  x^2=a(mod p) , do I get to conclude that there are no solutions to x^2=a(mod p^2), and so on?

    Well, trivially: if x^2=a\!\!\pmod{p^2} , then x^2=a+kp^2=a+(kp)p\Longrightarrow x^2=a\!\!\pmod p...

    Tonio
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