查询词典 Fermat number

Main work follows:(1) In the first part of this paper, a historical development of the number theory before Gauss is reviewed.Based on the systematic analysis of Gauss"s work in science and mathematics, inquiry into the mathematical background that Disquisitiones Arithmeticae appeals and Gauss"s congruent theory;(2) The development process of Fermat"s little theorem and its important function in the compositeness test is elaborated through original literature.we think that the first three section of Disquisitiones Arithmeticae is a summary and development for ancestors" work about Fermat"s little theorem,show that Fermat"s little theorem played an important role in the elementary number theory;(3) With the two main sources of the quadratic reciprocity law, investigating Fermat,Euler,Lagrange,Legendre, until the related work of Gauss,the way to realize the laws huge push to the development of algebraic number theory in 19 centuries.

本文主要做了以下工作：(1)首先回顾了高斯之前的数论研究状况，在系统分析高斯的科学与数学成就的基础上，探讨了《算术研究》出现的数学背景和高斯的同余理论；(2)通过对原始文献的系统解读，深入分析了费马小定理发现发展的历程以及在素性检验中的重要作用，指出《算术研究》前三节是高斯在总结并发展了前人对该定理研究的基础上形成的，并揭示了费马小定理在初等数论定理证明中的核心地位；(3)以二次互反律的两个主要来源为线索，详细考察了费马，欧拉，拉格朗目，勒让德，直到高斯的相关工作，揭示了该定律对十九世纪数论发展的巨大推动作用。

The reasons announced for receiving the award:"for the developed of new number theoretic tools to help in the solution of known fundamental problems in number theory"; for "first proving the Fermat's last theorem" etc. total four reasons.

公布的颁奖理由是"开发了有助于解决数论领域知名基础性问题的新型数论工具""首先证明费马大定理"等4项。

Help the Distributed Search for Fermat Number Divisors project find unique Fermat Number factors.

协助Fermat因子网络搜寻计划寻找特别的费马数因子。

Every integer can be written uniquely as a product of prime factors, and that because the Fermat number are co-prime, each prime number can appear in at most one Fermat number.

每个整数都可以被独特得分解质因数，而且因为费马数是互质的，每一个质数最多只能在一个费马数中出现。

This deduction establishes the theory foundation for selection of unity roots when constructing discrete image data, and provides the corresponding theory for applying Fermat number transforms in image processing and other fields further.

为Fermat数变换在图像处理领域的应用提供了理论依据。

Number Theoretic Transform; Integer transform; Fermat number transforms; Discrete Image data

数论变换；整型变换； Fermat数变换；离散图象数据

In 2000, F. LUCA proved that Fermat number are anti-sociable numbers, and in 2005, M. H. LE proved all powers of 2 are anti-sociable numbers. We have used the method of M. H. LE to obtain some new results of the anti-sociable numbers. For every integer n containing prime divisors that are 1 mod 4, let p mod 4 be an arbitrary prime divisor of n. There is at least one anti-sociable number in n^2, p^2n^2, p^4n^2, and p^6n^2. Therefore we can prove that anti-sociable numbers have positive density in perfect square numbers. We also give a method to find the exact anti-sociable numbers.

LUCA证明了Fermat数都是孤立数；2005年，乐茂华教授证明了2的方幂都是孤立数，用乐茂华教授的方法给出孤立数的一些新的结果：对于任意含有4w+1型素因子的正整数n，设p为n的任意一个4w+1型素因子，则在n^2，p^2n^2，p^4n^2，p^6n^2里至少有一个是孤立数，因此可以证明孤立数在完全平方数里有正密度，另外也给出求解确定孤立数的方法。

This paper analyzes the property of FNT, the characteristics of Kernel Matrixes and the relationship between Kernel Matrixes of two-dimensional Fermat number transform whose modulus are odd prime and image data, and presents and proves the deduction of the theorem which demonstrates the relationship among different transform matrixes corresponding to different roots of unity under the same odd prime modulus of FNT, and reveals the essence of FNT whose modulus are odd prime.

分析二维Fermat数变换性质、正反变换核的特点、二维模为奇素数的二维Fermat数变换正反变换核以及与图像数据的关系，提出了不同单位根对应变换矩阵间的关系定理的推论，证明了该推论中模为奇素数的二维Fermat数变换的不同单位根对应的变换矩阵之间的关系，揭示了模为奇素数的二维Fermat数变换的本质，在构造离散图象数据Fermat数变换时为单位根的选择奠定了理论基础。

Presents the study of second order linear constant coefficient progressive regression equation with the latest achievements in the "greatest common divisor" theory to give the great significance of Fibonacci combination series equation, Fermat Number , and Mersenne Number, and a only exceptional value each.

用"最大公约数"理论的最新结果，研究二阶线性常系数齐次递归方程，给出斐波那契数列组合式、费马数、梅森数在组合数学上的重要意义和它各自有一个且唯一例外

Some of the oldest open problems in mathematics relate to the abundancy index of a number. Are there infinitely many perfect numbers? Does there exist an odd perfect number? Does there exist an odd multiply perfect number? Such questions have been considered for well over two millennia by the likes of Euclid, Fermat, Descartes, Mersenne, Legendre, and Euler.

暑期的数学研究已渐渐步入正轨，今天上午和导师讨论的时候提出了第一个conjecture，说是虽然6和12的倍数的abundancy index比较高，但是如果把两个相邻的数字相乘，他们乘积的abundancy index总体来说会甚至更高。

In the negative and interrogative forms, of course, this is identical to the non-emphatic forms.

。但是，在否定句或疑问句里，这种带有"do"的方法表达的效果却没有什么强调的意思。

Go down on one's knees;kneel down

屈膝跪下。。。下跪祈祷