Diophantine inequalities involving a prime and an almost-prime

Research output: Contribution to journalArticlepeer-review

Abstract

We prove that there are infinitely many solutions of|λ01p+λ2P3|<p−1131, where λ0 is an arbitrary real number and λ12∈R with λ2≠0 and 0>λ1λ2 not in Q. This improves a result by Harman.

Original languageEnglish (US)
Pages (from-to)347-367
Number of pages21
JournalJournal of Number Theory
Volume170
DOIs
StatePublished - Jan 1 2017
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Algebra and Number Theory

Keywords

  • Almost-primes
  • Diophantine inequalities
  • Sieve method

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