2016/04/30 by Prabhu, Neha
#11B25 #11D45 #11N37 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1605.00088
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 n not greater than x with k prime factors such that a fixed quadratic equation has exactly 2k solutions modulo n.