On the number of roots of an integral polynomial modulo \(q\)
The authors prove that the set of congruence classes modulo a power of a prime number which are roots of an integral polynomial with degree \(d\) is a collection of at most \(d\) arithmetical progressions. This result implies an upper bound on the number of these roots lying in a given small interval; such bounds are useful to study the number of points close to a smooth algebraic curve. The methods of proofs are combinatorial and make no use of Hensel's Lemma.
scientific article; zbMATH DE number 1229651