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.
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页码：423 / 430
页数：8
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