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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
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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
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3. Prachar, K., Primzahlverteilung (Berlin, 1957).Google Scholar