期刊文献+
共找到10篇文章
< 1 >
每页显示 20 50 100
方程φe(n)=n/d(e=1,2,4)的可解性 被引量:15
1
作者 王容 廖群英 《纯粹数学与应用数学》 2016年第5期481-494,共14页
利用已有的广义欧拉函数的准确计算公式来研究方程φe(n)的可解性,其中n为正整数,d为n的正因子.并利用初等的方法和技巧给出方程φe(n)=n/d(e=1,2,4)的全部正整数解(n,d).
关键词 广义欧拉函数 丢番图方程 正整数解
下载PDF
关于Makowski-Schinzel的一个猜想
2
作者 杨仕椿 《北华大学学报(自然科学版)》 CAS 2004年第2期106-107,共2页
设ψ(n),σ(n)分别是正整数n的Euler函数与约数和函数.证明了,如果n存在素因子p,使p2| n,则ψ(σ(n))/n>-1/2,从而完全解决了Makowski-Schinzel的一个猜想.
关键词 euler函数 约数和函数 下界 Makowski-Schinzel猜想
下载PDF
关于方程ф(x)=ф(y) 被引量:1
3
作者 张明志 《四川大学学报(自然科学版)》 CAS CSCD 1995年第6期628-631,共4页
设为Euler函数,R.D.Carmichael猜想:对每一正整数x,存在不等于x的正整数y,使得作者给出方程的解的结构,利用这种结构得到探求解的算法以及Carmichael猜想的反例所满足的一些条件,A.Schin... 设为Euler函数,R.D.Carmichael猜想:对每一正整数x,存在不等于x的正整数y,使得作者给出方程的解的结构,利用这种结构得到探求解的算法以及Carmichael猜想的反例所满足的一些条件,A.Schinzel猜想:对每个偶整数k,方程有无穷多解.作者证明:如果存在无穷多个素数p,使2p-1仍为素数,则Schinzel猜想成立. 展开更多
关键词 Carmichael猜想 Schinzel猜想 欧拉函数
下载PDF
Carmichael猜想的一个标注
4
作者 王恒洲 史三英 《合肥工业大学学报(自然科学版)》 CAS 北大核心 2020年第2期285-288,共4页
Carmichael猜想是数论的一个经典猜想,很多数学家都对该猜想做过各种研究。Carl Pomerance是第1个对该猜想进行理论研究的,并提出了该猜想的一个充分条件。通过引进φ-子集概念,文章研究了关于未知数n的方程φ(n)=x的解的个数,证明该猜... Carmichael猜想是数论的一个经典猜想,很多数学家都对该猜想做过各种研究。Carl Pomerance是第1个对该猜想进行理论研究的,并提出了该猜想的一个充分条件。通过引进φ-子集概念,文章研究了关于未知数n的方程φ(n)=x的解的个数,证明该猜想的一个充要条件为:Carmichael猜想成立当且仅当猜想在集{2^43^37^243k,k为任意正整数}上成立。 展开更多
关键词 Carmichael猜想 欧拉函数 φ-子集 素数 素因数集
下载PDF
Landau误差项和Sitaramachandrarao猜想的研究
5
作者 刘建亚 《宁夏大学学报(自然科学版)》 CAS 1993年第1期1-15,共15页
本文首先研究了Sitaramachandrarao猜想,然后分别改进了Sitaramachandr-arao引入的误差项E_1(x)和Landau误差项E_0(x)的算术均值和积分均值估计。
关键词 Landau误差项 S猜想 欧拉函数
下载PDF
猜想σ((n))/n≥1/2
6
作者 房剑平 《淮阴师范学院学报(自然科学版)》 CAS 2002年第4期17-20,共4页
本文证明了当k≤7,a1 >a2 > >ak>1,且ai+1 (i=1,2, ,k)是素数时,σ ∏ki=1ai ≥∏ki =1(ai+1 )成立,进而证明了当n素因子个数不超过 7时,猜想σ( (n))
关键词 因数和函数 欧拉函数 基本链 猜想σ(ф(n))/n≥1/2
下载PDF
The Prime Sequence: Demonstrably Highly Organized While Also Opaque and Incomputable-With Remarks on Riemann’s Hypothesis, Partition, Goldbach’s Conjecture, Euclid on Primes, Euclid’s Fifth Postulate, Wilson’s Theorem along with Lagrange’s Proof of It and Pascal’s Triangle, and Rational Human Intelligence
7
作者 Leo Depuydt 《Advances in Pure Mathematics》 2014年第8期400-466,共67页
The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The ma... The main design of this paper is to determine once and for all the true nature and status of the sequence of the prime numbers, or primes—that is, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, and so on. The main conclusion revolves entirely around two points. First, on the one hand, it is shown that the prime sequence exhibits an extremely high level of organization. But second, on the other hand, it is also shown that the clearly detectable organization of the primes is ultimately beyond human comprehension. This conclusion runs radically counter and opposite—in regard to both points—to what may well be the default view held widely, if not universally, in current theoretical mathematics about the prime sequence, namely the following. First, on the one hand, the prime sequence is deemed by all appearance to be entirely random, not organized at all. Second, on the other hand, all hope has not been abandoned that the sequence may perhaps at some point be grasped by human cognition, even if no progress at all has been made in this regard. Current mathematical research seems to be entirely predicated on keeping this hope alive. In the present paper, it is proposed that there is no reason to hope, as it were. According to this point of view, theoretical mathematics needs to take a drastic 180-degree turn. The manner of demonstration that will be used is direct and empirical. Two key observations are adduced showing, 1), how the prime sequence is highly organized and, 2), how this organization transcends human intelligence because it plays out in the dimension of infinity and in relation to π. The present paper is part of a larger project whose design it is to present a complete and final mathematical and physical theory of rational human intelligence. Nothing seems more self-evident than that rational human intelligence is subject to absolute limitations. The brain is a material and physically finite tool. Everyone will therefore readily agree that, as far as reasoning is concerned, there are things that the brain can do and things that it cannot do. The search is therefore for the line that separates the two, or the limits beyond which rational human intelligence cannot go. It is proposed that the structure of the prime sequence lies beyond those limits. The contemplation of the prime sequence teaches us something deeply fundamental about the human condition. It is part of the quest to Know Thyself. 展开更多
关键词 Absolute Limitations of Rational Human Intelligence Analytic Number Theory Aristotle’s Fundamental Axiom of Thought Euclid’s Fifth Postulate Euclid on Numbers Euclid on Primes Euclid’s Proof of the Primes’ Infinitude euler’s Infinite Prime Product euler’s Infinite Prime Product Equation euler’s Product Formula Godel’s Incompleteness Theorem Goldbach’s conjecture Lagrange’s Proof of Wilson’s Theorem Number Theory Partition Partition Numbers Prime Numbers (Primes) Prime Sequence (Sequence of the Prime Numbers) Rational Human Intelligence Rational Thought and Language Riemann’s Hypothesis Riemann’s Zeta function Wilson’s Theorem
下载PDF
An Equivalent Form of Strong Lemoine Conjecture and Several Relevant Results
8
作者 ZHANG Shaohua 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2019年第3期229-232,共4页
In this paper, we consider some problems involving Strong Lemoine Conjecture in additive number theory. Based on Dusart's inequality and Rosser-Schoenfeld's inequality, we obtain several new results and give a... In this paper, we consider some problems involving Strong Lemoine Conjecture in additive number theory. Based on Dusart's inequality and Rosser-Schoenfeld's inequality, we obtain several new results and give an equivalent form of Strong Lemoine Conjecture. 展开更多
关键词 Lemoine conjecture Dusart’s INEQUALITY Rosser-Schoenfeld’s INEQUALITY euler totient function primecounting function
原文传递
Strong Goldbach Conjecture and Generalized Moser-Type Inequalities
9
作者 ZHANG Shaohua 《Wuhan University Journal of Natural Sciences》 CAS CSCD 2021年第1期15-18,共4页
In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting function.Using computer,Pierre Dusart’s ine... In this paper,we consider the generalized Moser-type inequalities,sayφ(n)≥kπ(n),where k is an integer greater than 1,φ(n)is Euler function andπ(n)is the prime counting function.Using computer,Pierre Dusart’s inequality onπ(n)and Rosser-Schoenfeld’s inequality involvingφ(n),we give all solutions ofφ(n)=2π(n)andφ(n)=3π(n),respectively.Moreover,we obtain the best lower bound that Moser-type inequalitiesφ(n)>kπ(n)hold for k=2,3.As consequences,we show that every even integer greater than 210 is the sum of two coprime composite,every odd integer greater than 175 is the sum of three pairwise coprime odd composite numbers,and every odd integer greater than 53 can be represented as p+x+y,where p is prime,x and y are composite numbers satisfying that p,and x and y are pairwise coprime.Specially,we give a new equivalent form of Strong Goldbach Conjecture. 展开更多
关键词 Strong Goldbach conjecture pairwise coprime euler totient function prime-counting function
原文传递
Composite Integers n for Which φ(n)|n-1 被引量:1
10
作者 William D.BANKS Florian LUCA 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2007年第10期1915-1918,共4页
In this note, we show that the number of composite integers n ≤ x such that φ(n)|n - 1 is at most O(x^1/2(loglog x)^1/2), thus improving earlier results by Pomerance and by Shan.
关键词 euler function lehmer conjecture
原文传递
上一页 1 下一页 到第
使用帮助 返回顶部