chebЧебышевский сборникChebyshevskii Sbornik2226-8383Tula State Lev Tolstoy Pedagogical University10.22405/2226-8383-2016-17-4-180-184cheb-295Research ArticleСтатьиArticlePROBLEM OF NESTERENKO AND METHOD OF BERNIKPROBLEM OF NESTERENKO AND METHOD OF BERNIKBudarinaN. V.BudarinaN. V.

(Khabarovsk)

(Khabarovsk)

O’DonnellH.O’DonnellH.

(Dublin)

(Dublin)

Khabarovsk Division of Institute for Applied MathematicsРоссияKhabarovsk Division of Institute for Applied MathematicsRussian FederationDublin Institute of TechnologyРоссияDublin Institute of TechnologyRussian Federation201615062017174180184Copyright © Budarina N.V., O’Donnell H., 20172017Budarina N.V., O’Donnell H.Budarina N.V., O’Donnell H.Данная работа распространяется под лицензией Creative Commons Attribution 4.0.This work is licensed under a Creative Commons Attribution 4.0 License.https://www.chebsbornik.ru/jour/article/view/295

In this article we prove that, if integer polynomial Psatisfies |P(w)|p< H−w, then for  > 2n− 2 and sufficiently large H the root belongs to the field of p-adic numbers.

In this article we prove that, if integer polynomial Psatisfies |P(w)|p< H−w, then for w > 2n− 2 and sufficiently large H the root belongs to the field of p-adic numbers.

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The authors declare that there are no conflicts of interest present.