Statement
Let be a polynomial with integer (or p-adic integer) coefficients, and let m,k be positive integers such that m ≤ k. If r is an integer such that
- and
then there exists an integer s such that
- and
Furthermore, this s is unique modulo pk+m, and can be computed explicitly as
- where
In this formula for t, the division by pk denotes ordinary integer division (where the remainder will be 0), while negation, multiplication, and multiplicative inversion are performed in .
As an aside, if, then 0, 1, or several s may exist (see Hensel Lifting below).
Read more about this topic: Hensel's Lemma
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