PulseExploreJournal ClubDebatesTrendingResearchersJournals
Instagram
HomeExploreJournal ClubTrending
Synapse
⌘+K
Synapse
February 27, 20260 citations

A Diophantine inequality with one prime of the form

View Full Paper
YLYukun LiuJHJing Huang

Key Points

  • The aim is to establish solutions to a specific Diophantine inequality involving prime numbers.
  • Defined a range for a constant c based on parameters s and N.
  • Assumed the existence of sufficiently large N and arbitrarily small ε.
  • Considered primes of the form p1 = m2 + n2 + 1.
  • Proved the existence of solutions for the Diophantine inequality when s is greater than or equal to 7.
  • Identified conditions under which specific combinations of primes can satisfy the inequality.

Abstract

Let 1 0 is a large enough number and ε > 0 is an arbitrarily small constant. This paper establish that the Diophantine inequality |p1c + … + psc − N | < ε has a solution in prime numbers p1,…,ps, where s ≥ 7 and s is a natural number and p1 can be expressed as p1 = m2 + n2 + 1 for some integers m,n.

Ask AI
Helpful
Bookmark
Share
View Full Paper

Cite This Study

Liu et al. (2026) studied this question.

synapsesocial.com/papers/69a13591ed1d949a99abf9b7https://doi.org/10.1051/ita/2026002/pdf
Ask AI
Helpful
Bookmark
Share
View Full Paper