费马

By reviewing carefully original literature,it is pointed out that pursing a more general reciprocity law maby the most motive of the development of algebraic number theory, usual material mainly emphasizes the function of Fermats last theorem.

通过原始文献的深入分析，研究表明：一般互反定律的寻求可能是代数数论发展的最主要动力，而通常文献中主要强调了费马大定理的作用。

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。

In this thesis, sound wave path equation is derived from Fermat's theorem and the calculus of variations, and then the temperature field is reconstructed by the combination least-square method and the modified sound wave path.

本文通过求解由费马定理和变积分原理确定的声波路径方程，结合最小二乘法实现了声波路径的修正。

However, based on my understanding of Jiang Chun-xuan's analysis and the preprint of his new paper "Disproof Of Wiles' Proof For Fermat's Last Theorem", I believe that I am in the position to make some important remarks, which provide strong support to Jiang's disproof of "Wiles's Proof For Fermat's Last Theorem" as follows

然而，基于我对于蒋春暄的分析及其新的文章"对怀尔斯费马大定理证明之否定"预印本的理解，我相信我有条件提出一些重要的看法，可以对蒋春暄否定"怀尔斯费马大定理证明"的文章给予重要支持

One is the Fermat's last theorem, one is the theoretical physics, two questions have nothing to do with one another!

一个是费马大定理，一个是理论物理，两个问题风马牛不相及！

A few overseas mathematical researchers indicated, after Jiang Chun-xuan writes the "Disprove Wiles' Proof of Fermat's Last Theorem", they would like together with Jiang Chun-xuan's proof of FLT published in China in early 1992, carefully review them together with other mathematicians of their country.

国外几位数学研究者表示，等蒋春暄将《怀尔斯对费马大定理的证明之否定》论文写出来以后，他们愿意将它与蒋春暄1992年初在中国发表的对费马大定理的证明论文一起与本国的数学家共同认真研究。

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。

Fermat s little theorem is one of the important theorems in number theory,but there has been little discussion in geometric field about it.

费马小定理是数论中的一个重要定理，但对其几何意义的论述几乎没有，给出了费马小定理的几何意义。

The concept of exponential transformations of rectangular Cartesiancoordinates is introduced, showing that a plane curve is more frequently expressed by a unionof four or fewer quadrantal equations defined uniquely in the respective quadrants whichthe curve covers and are therefore quadrant invariant, then the Fermat curve s with someof their geometric properties are formulated.

引入直角笛卡儿坐标幂变换的概念，说明一平面曲线是较经常地用4个或更少的象限方程的并集来表示的；这些象限方程是在曲线所在的各个象限中惟一定义的，因而是象限不变的。然后列出费马曲线的方程，并简述了费马曲线的一些几何性质

The Fermat"s principle, Fresnel"s coefficients, Goos-Hanchen effect and Brewster angle at an interface between a PIM and a NIM were studied respectively. When the NIMs are introduced, the two traditional descriptions of Fermats principle are not consistent with each other and the least time principle do not hold true anymore.

随着负折射率介质的引入通过对费马原理的两种传统描述形式的研究可以发现，正—负折射率介质平界面处的最短时间原理已不成立，并进一步验证了使用光程表达的费马原理才是严格的正确的理论。

With Death guitarist Schuldiner adopting vocal duties, the band made a major impact on the scene.

随着死亡的吉他手Schuldiner接受主唱的职务，乐队在现实中树立了重要的影响。

But he could still end up breakfasting on Swiss-government issue muesli because all six are accused of nicking around 45 million pounds they should have paid to FIFA.

不过他最后仍有可能沦为瑞士政府&议事餐桌&上的一道早餐，因为这所有六个人都被指控把本应支付给国际足联的大约4500万英镑骗了个精光。