查询词典 Fermat

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。

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

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。

In this paper, we mainly study the alternating group A_4 actions on spin 4-manifolds. First we discuss the special action of A_4 on K3 surfaces of Fermat type, we compute the fixed points set of this action and some invariants of the group action, also we get some topological properties. Then we study the A_4 actions on general K3 surfaces and obtain some similar results.

本文主要是以交错群A_4在K3曲面上的作用为研究对象，从Fermat型K3曲面上的特殊的A_4作用出发，得到了Fermat型K3曲面上A_4作用的不动点，利用不动点集计算了群作用的一些不变量并得到了相关的拓扑性质，在此基础上进一步把其中的一些结果推广到一般情形下的同伦K3曲面上。

Refraction regularity of extraordinary ray in uniaxial crystal with arbitrarily oriented optical axis;2. In the case of optical axis of uniaxial crystal being parallel with the incident plane, the angle of refraction of extraordinary ray are calculated by using Fermat's principle.

在单轴晶体的光轴与入射面平行的情形下用费马原理计算非寻常光光线的折射角，然后就怎样定义非寻常光作些讨论，最后在单轴晶体的光轴任意取向的普遍情形下给出计算非寻常光光线折射方向的公式。

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。

Descartes and Fermat were both proponents of a corpuscular theory; Huygens'believed in a wave theory.

笛卡尔和 Fermat 都是微粒子学说理论的支持者； Huygens 相信波动说。

When propagating light\|ray passes through two fixed points in the gradient index mediums and a cuspidal variable\|point （at this point the trace equation of propagating light\|ray is non\|differentiable） at the borderline of two different GRIN mediums, the mathematical relationship, which the trace equation of propagating light\|ray and borderline equation of two different GRIN mediums should satisfy, is derived by the Fermat's principle and calculus of variation.

当光线通过梯度折射率介质中两个固定点和两个GRIN介质界线上的可动尖点（光线轨迹方程的不可微点）时，由费马原理和变分法运算推得传输光线的轨迹方程与两种不同GRIN介质的界线方程应满足的微分关系式。

About this, Pierre de Fermat wrote in 1637 in his copy of Diophantus's Arithmetica,"I have discovered a truly remarkable proof but this margin is too small to contain it."

G.Bachet所翻译的丢番图《算术》中写道︰「我已发现了一个真正不凡的证明，但页边太小，写不下。

There are different types of personal loans available.

有许多不同类型的个人贷款优惠。

The above mentioned teaching model of spiral rising can be used to avoid rigidness in teaching.

上述螺旋式上升的教学模式，可以避免教学形成模式後的僵化现象。