FUNDAMENTALNAYA I PRIKLADNAYA MATEMATIKA

(FUNDAMENTAL AND APPLIED MATHEMATICS)

1997, VOLUME 3, NUMBER 1, PAGES 163-170

Additive problems with numbers having a given number of prime dividers from progressions

A. A. Zhukova

Abstract

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We have found the number of the representations of a number N as

n=mr    and    n+m2+r2,

where m,r -- natural numbers and n are the numbers having k prime dividers such that pi º li( mod d0), pi ³ t > lnB+1N, (li,d0)=1, i=1,2, ¼ ,k, (N-l1 ¼ lk,d0)=1. The paper also contains the results about distribution of such numbers n in arithmetic progressions with large modulus.


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