Hensel's Lemma Interactive Game

🎓 What is Hensel's Lemma?

Hensel's lemma is a powerful technique in number theory that allows us to "lift" solutions from modulo p to modulo p^k. It's like having a mathematical elevator!

The Main Idea: If we have a root r of polynomial f(x) modulo p, and the derivative f'(r) ≢ 0 (mod p), then we can find a unique root modulo p² that reduces to r modulo p.

r_k+1 = r_k - f(r_k) × [f'(r_k)]^-1 (mod p^k+1)

This is essentially Newton's method in the p-adic numbers! Let's learn by solving problems together.

Level 1

Score: 0

25%

🎯 Current Problem

Polynomial: f(x) = ?

Prime: p = ?

🔍 Step 1: Find Roots Modulo p

First, let's find all roots of f(x) ≡ 0 (mod p):

🧮 Hensel's Lemma Game

🎓 What is Hensel's Lemma?