On the number of special numbers

被引：3

作者：

Aktas, Kevser ^{[1
]}

Murty, M. Ram ^{[2
]}

机构：

[1] Gazi Univ, Dept Math Educ, TR-06500 Ankara, Turkey

[2] Queens Univ, Dept Math & Stat, Kingston, ON K7L 3N6, Canada

来源：

PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES | 2017年 / 127卷 / 03期

基金：

加拿大自然科学与工程研究理事会;

关键词：

Special numbers; squarefull numbers; Thue-Mahler equations; abc conjecture; ABC-CONJECTURE;

D O I：

10.1007/s12044-016-0326-z

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For lack of a better word, a number is called special if it has mutually distinct exponents in its canonical prime factorizaton for all exponents. Let V(x) be the number of special numbers <= x. We will prove that there is a constant c > 1 such that V(x) similar to cx/log x. We will make some remarks on determining the error term at the end. Using the explicit abc conjecture, we will study the existence of 23 consecutive special integers.

引用

页码：423 / 430

页数：8

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