# Math Help - Hensel's lemma

1. ## 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?

2. Originally Posted by Chris11
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