On the distribution of \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} \(\sqrt p\) \end{document} modulo one involving primes of special type

Author:

Cai Yingchun1

Affiliation:

1. 1 Tongji University Department of Mathematics Shanghai 200092 P. R. China

Abstract

Let Pr denote an almost-prime with at most r prime factors, counted according to multiplicity. In this paper we show that the inequality \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\left\{ {\sqrt p } \right\} < p^{ - \tfrac{1} {{15.5}}}$$ \end{document} has infinitely many solutions in primes p such that p + 2 = P4.

Publisher

Akademiai Kiado Zrt.

Subject

General Mathematics

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4. On the representation of a large even integer as the sum of a prime and the product of at most two primes;Chen J. R.;Sci. Sin,1973

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