The Number of Integers Divisible by a^k Except a^(k+l) b

Authors

  • Yanapat Tongron Mathematics and Applied Statistics Program, Faculty of Science and Technology, Nakhon Ratchasima Rajabhat University, Nakhon Ratchasima 30000, Thailand
  • Kanyaphak Paikhlaew Mathematics and Applied Statistics Program, Faculty of Science and Technology, Nakhon Ratchasima Rajabhat University, Nakhon Ratchasima 30000, Thailand

Keywords:

Bounds, Ceiling function, Divisibility, Floor function, Integer

Abstract

For positive integers gif.latex?a,b,k,l,n, let gif.latex?A_{(k,l)}^{(a,b)}(n) be the set of all integers divisible by gif.latex?a^{k} except gif.latex?a^{k+l}b between gif.latex?1 and gif.latex?n. Under certain condition on these integers, we obtain the explicit formula for gif.latex?\left&space;|A_{(k,l)}^{(a,b)}(n)&space;\right&space;|, where gif.latex?\left&space;|X&space;\right&space;| denotes the number of elements in a finite set gif.latex?X. We also provide bounds on gif.latex?\left&space;|A_{(k,l)}^{(a,b)}(n)&space;\right&space;| and show that these are the best bounds by examples.

Downloads

Download data is not yet available.

Downloads

Published

2022-09-28

How to Cite

Tongron , Y., & Paikhlaew, K. (2022). The Number of Integers Divisible by a^k Except a^(k+l) b. Science & Technology Asia, 27(3), 132–136. Retrieved from https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/242455

Issue

Section

Physical sciences