Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-16T01:54:02.080Z Has data issue: false hasContentIssue false
  • English
  • Français

On the Integral Part of a Linear form with Prime Variables

Published online by Cambridge University Press:  20 November 2018

I. Danicic
I. Danicic*
Affiliation:
Bedford College, London University
Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The object of this paper is to prove the following:

Theorem. Suppose that λ, μ are real non-zero numbers, not both negative, λ is irrational, and k is a positive integer. Then there exist infinitely many primes p and pairs of primes p1, p2 such that

In particular [λp1 + μp2] represents infinitely many primes.

Here [x] denotes the greatest integer not exceeding x.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 18 , 1966 , pp. 621 - 628
Copyright
Copyright © Canadian Mathematical Society 1966

References

1. Davenport, H. and Heilbronn, H., On indefinite quadratic forms in five variables, J. London Math. Soc., 21 (1946), 185–193.Google Scholar
2. Davenport, H. and Roth, H., The solubility of certain Diophantine inequalities, Mathematika, 2 (1955), 81–96.Google Scholar
3. Prachar, K., Primzahlverteilung (Berlin, 1957).Google Scholar