This chapter consists of elementary number theory and deals with the greatest common divisor, the euclidean algorithm, congruences, linear equations, primitive roots, and the quadratic reciprocity law. The material covered here corresponds to the first four chapters of Gauss's Disquisitiones arithmeticae...
这书可以说是数论第一本有系统的著作,高斯第一次介绍“同余”(Congrudent)这个概念(现在的中学“新数学”就有教这玩意儿)。而且还有数论上很重要的高斯称为“数论的酵母”的“二次互逆定理”(Law of Quadratic reciprocity)。这定理是描述一对素数的美丽关系,欧拉和勒让得知道这些关系,但没有法子证明。高斯在18...
(2)二次互反律的证明 8 Gauss二次互反律--经典证明 9 Gauss二次互反律--经典证明 10 Gauss二次互反律--经典证明 11 Gauss二次互反律--经典证明 12 Gauss二次互反律--经典证明 13 Gauss二次互反律简证 2、Gauss二次互反律简证 WouterCastryck Ashortenedclassicalproofofthequadraticreciprocity law,...
1. What is a Reciprocity Law?[J].B. F. Wyman,The American mathematical monthly.1972,第6期 2. 数论导引[M].华罗庚.1975 3. 解析数论基础[M].潘承洞; 潘承彪; 著.1991 上一页 1 下一页 相似文献 中文文献 外文文献 专利 1. Legendre符号及Gauss二次互反律的证明 [J] . 郭向荣...
而且还有数论上很重要的高斯称为“数论的酵母”的“二次互逆定理”(Law of Quadratic reciprocity)。这定理是描述一对素数的美丽关系,欧拉和勒让得知道这些关系,但没有法子证明。高斯在18岁时重新发现并给了第一个证明,他认为这是数论的“宝石”,一生给出五个不同证明。 在天文学上的卓越贡献 24岁开始,高斯...
–Quadratic Reciprocity Law; –at 21 wrote the Number Theory masterpiece“Disquisitiones Arithmeticae” (Latin, Arithmetical Investigations). Gauss Nephew and Maternal Uncle July 3, 2013tomcircleChinese,Education1 Comment There is a common proverb in my Chinese dialect Fujian spoken today in China Fuji...
Legendre符号及Gauss二次互反律的证明
Gauss also made important contributions to number theory with his 1801 bookDisquisitiones arithmeticae, which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity. He had been supported by a stipend from the Duke of Brunswick, but he did not...
reciprocity laws 互反律〔找d户心钾h邢;.a枷,oeT,3翻服] 在幕剩余(po袱江residue)符号之间或者范剩余符号(~一心记璐s帅加l)之间的一些关系. 如下最简单表述的互反律,在P,Fen刃日t时已知,能除得尽数扩十1的素数只有2和算术级数4k+1中的素数,换句话说,等式 xZ+l三0(n扣吐夕),其中P>2的素数可解...
Finally, Gauss Lemma and Law of Quadratic Reciprocity are proven.MML identifier: INT 5, version: 7.8.05 4.89.993 In this paper, we defined the quadratic residue and proved its fundamental properties on the base of some useful theorems. Then we defined the Legendre symbol and proved its ...