Czechoslovak Mathematical Journal

, Volume 67, Issue 2, pp 439–455

Density of solutions to quadratic congruences

Article
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Abstract

A classical result in number theory is Dirichlet’s theorem on the density of primes in an arithmetic progression. We prove a similar result for numbers with exactly k prime factors for k > 1. Building upon a proof by E.M. Wright in 1954, we compute the natural density of such numbers where each prime satisfies a congruence condition. As an application, we obtain the density of squarefree nx with k prime factors such that a fixed quadratic equation has exactly 2k solutions modulo n.

Keywords

Dirichlet’s theorem asymptotic density primes in arithmetic progression squarefree number 

MSC 2010

11D45 11B25 11N37 

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References

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Copyright information

© Institute of Mathematics of the Academy of Sciences of the Czech Republic, Praha, Czech Republic 2017

Authors and Affiliations

  1. 1.Indian Institute of Science Education and ResearchPuneIndia

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