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

Yanapat Tongron; Kanyaphak Paikhlaew

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已出版: 9月 28, 2022

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

摘要

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.

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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. 取读于从 https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/242455

期

Vol.27 No.3 (July-September 2022)

栏目

Physical sciences

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