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同余概念是数论中的一个重要组成部分，利用同余的定义、定理及一些性质，可以检验整数的整除性及整数的加法，整数的乘积运算结果等；利用费马定理，进行素数、合数的判别是一个很有效的方法。 相似文献
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(本讲适合高中)
同余是初等数论的重要组成部分,在处理整除性、整数分类、解不定方程等数学竞赛问题中起到重要作用,其相关的定理也是解决数论问题的重要工具.本文给出同余的定义及常用定理,并通过近几年的竞赛题举例,从解题的思路分析,说明同余思想在数学竞赛中的应用. 相似文献
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本文研究了初等数论课程的历史及发展现状,简要介绍了整数理论、同余理论及方程理论的发展历史,并介绍了"中国剩余定理"及著名的"费马大定理"。 相似文献
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同余是解决数学问题的一个有力的工具,本文就利用整数的同余关系及其性质分别寻找了能被16,12,8整除的一个条件． 相似文献
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不定方程的求解是数论学习的重要内容,利用同余与同余式解不定方程是不定方程求解的常用方法.利用一次同余式、二次同余式与同余性质解不定方程的一般方法,对求不定方程整数解的学习难点有所帮助. 相似文献
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一元一次同余方程的求解关键在于求解有唯一解的一元一次同余方程 ,利用同余的概念、同余的性质、余数定理等 ,可得到有唯一解的一元一次同余方程的五种求解办法 相似文献
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Wilson定理的重要性,不仅表现在对二次同余的研究有帮助,而且它给出一个正整数是素数的充要条件,因而决定一个正整数是否为素数的问题已经完全解决.本文将利用多项式除法给出Wilson定理的另一种证明. 相似文献
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有关相邻两整数之积的问题,经常出现在数学竞赛题之中.本文将给出一个判定某数是相邻两整数之积的定理,并利用它来解决一些有关的问题.定理万是相邻两整数之积的充要条件是4M十1为完全平方数. 证明先证必要 相似文献
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（本讲适合高中）
同余是数论的重要概念,其性质及相关重要定理是解决数论问题的重要工具．本文给出同余的定义与定理,并举例说明其应用． 相似文献
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沈景清 《通化师范学院学报》1997,(8)
通过本文的论征,主要推广了余数定理和Hamilton—Cayley定理的结论,同时还揭示了Hamilton—Cayley定理与数α是一元多项式f(x)的根的充要性定理之间的联系,他们都是同一个定理的特殊情形。 相似文献
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Shivam Kumar 《Resonance》2007,12(9):25-39
Are there perfect squares which on division by 7 leave remainder 3? Are there perfect squares which on division by 3 leave
remainder 7? (A “remainder of 7” on division by 3 is the same as a remainder of 1.) The answers: ‘NO’ and ‘YES’, respectively.
These facts are stated by number theorists as follows: 3 is a quadratic non-residue modulo 7; 7 is a quadratic residue modulo 3. The notion of quadratic residue is far reaching, and the key theorem here is the Law of Quadratic Reciprocity, first stated
by Euler in 1783, but without proof, and first proved by Gauss, in 1796. The theorem is easy to state but is mysterious, as
it reveals a connection between two questions that appear unconnected. Let p, q be distinct odd primes; then the questions are: “Is p a quadratic residue modulo q?” and “Is q a quadratic residue modulo p?” Gauss had a high regard for this result and called it Theorema Aureum, the Golden Theorem. Though it has been proved in many different ways, it retains its mystery. In this two part article we
give three proofs of the theorem. The first one, described in this part, is based on group theory. 相似文献
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Stephen W. Rainbow Eugene Sadler-Smith 《British journal of educational technology : journal of the Council for Educational Technology》2003,34(5):615-624
Computer‐assisted learning (CAL) is becoming ever more important as a method of teaching and facilitating learning in an increasingly overburdened higher education sector in the UK. A number of authors have made pleas for more evaluation and research in the area of CAL. This study set out to evaluate the attitudes to CAL amongst over 300 business and management undergraduates using a questionnaire survey. The survey revealed a positive disposition towards CAL irrespective of age, gender or educational background. In addition respondents were asked to compare the features of CAL with those of other more traditional methods of teaching and learning. Two factors were identified, labelled CAL ‘instructional’ features and CAL ‘tutorial’ features. The instructional features of CAL were rated more highly than its tutorial features. Respondents rated CAL as better than traditional methods in terms of its instructional features and about the same as traditional methods in terms of its tutorial features. Younger respondents rated the instructional features of CAL more highly than did the older respondents. The findings were discussed in terms of their implications for the use of CAL in an expanding system of mass higher education. 相似文献
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讨论了一般线性同余方程组的求解问题,给出了一般同余方程组在有解情形下解的统一的表达式,得到了几个有益的结果,在理论上作了一种新的尝试,从而推广了孙子定理. 相似文献
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Time allocation scheme in IEEE 802.15.3 TDMA mechanism 总被引：1，自引：0，他引：1
In network with a shared channel in TDMA mechanism, it is a core issue to effectively allocate channel time to provide service guarantees for flows with QoS requirements. This paper proposes a simple and efficient time allocation scheme called MES-ESRPT (MCTA at the End of Superframe-Enhanced Shortest Remaining Processing Time) for delay-sensitive VBR traffic in accordance with IEEE 802.15.3 standard. In this algorithm, PNC (piconet coordinator) allocates one MCTA (Management Channel Time Allocation) for each stream which is the process of communication at the end of superframe. During the MCTA period, each transmitter should report current fragments number of the first MSDU (MAC Service Data Unit) and the fragments number of the remainder MSDUs to PNC. In the next superframe, PNC firstly allocates part CTAs (Channel Time Allocation) for each stream based on the remainder fragments number of the first MSDU by SRPT rule, then allocates remainder CTAs for each stream based on all fragments number of remainder MSDUs by the same SRPT rule. Simulation results showed that our proposed MES-ESRPT method achieves significantly better performance in QoS for multimedia streams compared to the existing schemes. 相似文献