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Sur les plus grands facteurs premiers inférieur à y d’entiers consécutifs

  • Zhiwei WangEmail author
Article
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Abstract

Let \(P_y^+(n)\) denote the largest prime factor p of n with \(p\leqslant y\). We prove that there exists a positive proportion of integers n such that \(P_y^+(n)<P_y^+(n+1)\) for \(y=x^{\alpha }\) when \(\alpha \) is small. Especially, the proportion is larger than 1 / 4 when \(\alpha \) tends to 0, which improves our previous result.

Keywords

Largest prime factor Consecutive integers Positive proportion Sieve 

Mathematics Subject Classification

Primary 11N25 Secondary 11K65 

Notes

Acknowledgements

Ce travail a été réalisé sous la direction de mes directeurs de thèse Cécile Dartyge et Jie Wu. Je les remercie vivement pour les nombreuses suggestions cruciales qu’ils ont proposées dans l’élaboration de ce travail.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsShandong UniversityJinanChina
  2. 2.Institut Élie Cartan de LorraineUniversité de Lorraine, UMR 7502Vandœuvre-lès-NancyFrance

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