Number Theory | Solving Polynomial Congruences with Hensel's Lemma

We give an example of solving a polynomial congruence modulo a power of a prime. We use Hensel's Lemma.

[kristianthulin]

The missing part:
y ≡ 3 (mod 5)
gives the new solution
4 + 3·5 = 19 (mod 25)
L = {3, 19}

[PunmasterSTP]

Lemma get another look at this stuff, 'cause I'm finding it a bit confusing. But definitely not because you didn't explain it well; this was another phenomenal video as always!

[Utesfan]

Mod 5: x^2+3x+2=(x+2)(x+1), so x =-2=3 or x=-1=4.

[georgesadler]

Professor Penn, thank you for a great lecture on solving Polynomials Congruences with Hensel's Lemma.

[markolastovcic]

I've tried solving this example using your alghoritm, I get 37 and 12 as solutiouns, but it should be 306 instead od 12. How do you get 306?

[ramzanmughal]

Which book you used...?please tell me the name of book....?

[lalalanding]

We could get y = 5 too right? not just 0 ?

[orlandomathlearningacademy]

Can we solve this without Hansen Lemma?