Fix f (t) ∈ Z[t] having degree at least 2 and no multiple roots. We prove that as k ranges over those integers for which the congruence f (t) ≡ 0 (mod k) is solvable, the least nonnegative solution is almost always smaller than k/(log k) c f . Here c f is a positive constant depending on f . The proof uses a method of Hooley originally devised to show that the roots of f are equidistributed modulo k as k varies.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.