河南科学
河南科學
하남과학
HENAN SCIENCE
2013年
1期
21-24
,共4页
Smarandache函数%伪Smarandache函数%整数解
Smarandache函數%偽Smarandache函數%整數解
Smarandache함수%위Smarandache함수%정수해
Smarandache function%pseudo-Smarandache function%integer solution
对任意正整数n,著名的Smarandache函数S(n)定义为最小的正整数m,使得n│m!.对于任意给定的正整数n,伪Smarandache函数Z(n)定义为最小的正整数m,使得n│1+2+…m=m(m+1).对任意正整数n,伪Smarandache无2平方因子函数Zw(n)定义为最小的正整数m,满足n│mn,即Zw(n)=min{m∶m∈N,n│mn}.用初等方法研究了方程S(n)+Z(n)=n和Zw(Z(n))-Z(Zw(n))=0并给出了它们的全部解.
對任意正整數n,著名的Smarandache函數S(n)定義為最小的正整數m,使得n│m!.對于任意給定的正整數n,偽Smarandache函數Z(n)定義為最小的正整數m,使得n│1+2+…m=m(m+1).對任意正整數n,偽Smarandache無2平方因子函數Zw(n)定義為最小的正整數m,滿足n│mn,即Zw(n)=min{m∶m∈N,n│mn}.用初等方法研究瞭方程S(n)+Z(n)=n和Zw(Z(n))-Z(Zw(n))=0併給齣瞭它們的全部解.
대임의정정수n,저명적Smarandache함수S(n)정의위최소적정정수m,사득n│m!.대우임의급정적정정수n,위Smarandache함수Z(n)정의위최소적정정수m,사득n│1+2+…m=m(m+1).대임의정정수n,위Smarandache무2평방인자함수Zw(n)정의위최소적정정수m,만족n│mn,즉Zw(n)=min{m∶m∈N,n│mn}.용초등방법연구료방정S(n)+Z(n)=n화Zw(Z(n))-Z(Zw(n))=0병급출료타문적전부해.
@@@@For any positive integer n,the famous Smarandache function S(n) is defined as the smallest positive integer m such that n│m! . The Pseudo-Smarandache function Z(n) is defined to be the smallest positive integer m such that n│1+2+…+m=m(m+1)2 . The Pseudo-Smarandache function Zw(n) is defined to be the smallest positive integer m such that n│mn . The main purpose of this paper is to use the elementary method to study the equation S(n)+Z(n)=n and Zw(Z(n))-Z(Zw(n))=0,and all solutions for them are given.
