On a combinatorial method for counting smooth numbers in sets of integers

被引：3

作者：

Croot, Ernie

机构：

来源：

JOURNAL OF NUMBER THEORY | 2007年 / 126卷 / 02期

基金：

美国国家科学基金会;

关键词：

D O I：

10.1016/j.jnt.2007.01.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we develop a method for determining the number of integers without large prime factors lying in a given set S. We will apply it to give an easy proof that certain sufficiently dense sets A and B always produce the expected number of "smooth" sums a + b, a epsilon A, b epsilon B. The proof of this result is completely combinatorial and elementary. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：237 / 253

页数：17

共 14 条

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