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

View as HTML     View as gif image    View as LaTeX source

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

where $m,r$ -- natural numbers and $n$ are the numbers having $k$ prime dividers such that $p$_i º l_i( mod d₀), $p$_i ³ t > ln^B+1N, $(l$_i,d₀)=1, $i=1,2,$¼ ,k, $(N-l$₁ ¼ l_k,d₀)=1. The paper also contains the results about distribution of such numbers $n$ in arithmetic progressions with large modulus.

All articles are published in Russian.

Location: http://mech.math.msu.su/~fpm/eng/97/971/97114h.htm
Last modified: November 16, 1999