爱德华·卢卡斯Édouard Lucas

爱德华·卢卡斯在亚眠的巴黎高等师范学校接受教育。此后，他在于尔班·勒维耶手下于巴黎天文台工作。

在普法战争（1870—1871）期间，卢卡斯担任炮兵军官。法国战败后，卢卡斯成为巴黎圣路易中学的数学教授。他后来又在巴黎查理曼中学任数学教授。

卢卡斯最著名的是他在数论中的结果：特别是他研究了斐波那契数列，相关的卢卡斯序列以他的名字命名。他给出了斐波那契数$\sqrt 5 f_{n} = \left(\Large\frac{1 + \sqrt 5}{2}\right)^{n}\normalsize - \left(\Large\frac{1 - \sqrt 5}{2}\right)^{n}$的著名公式。卢卡斯还设计了测试素性的方法，基本上就是今天所用的那些。1876年，他用他的方法证明了马兰·梅森数$2^{127} - 1$是prime。这仍然是在没有计算机辅助的情况下发现的最大素数。

卢卡斯的素数测试在1930年被德里克·亨利·莱默改进。它的工作原理如下。定义序列$S_{2} = 4, S_{3} = 14, S_{4} = 194, . . .$，其中对于$n > 2, S_{n}$由$S_{n} = S_{n-1}^{2} - 2$归纳定义。卢卡斯-德里克·亨利·莱默测试表明，一个马兰·梅森数$M_{p} = 2^{p} - 1$，其中$p > 2$，是素数当且仅当$M_{p}$整除$S_{p}$。

卢卡斯证明了$S_{127}$可被$M_{127}$整除，从而表明$M_{127}$是素数。这是一个极其困难的计算，因为$M_{127}$是一个大数，而$S_{127}$大得难以置信。事实上，$M_{127}$ = 170141183460469231731687303715884105727，而卢卡斯之所以能够进行这个计算，是因为他证明了$S_{127}$可被$M_{127}$整除，而无需计算$S_{127}$。

卢卡斯还因发明汉诺塔谜题及其他数学游戏而闻名。汉诺塔谜题于1883年以M. Claus之名出现。注意，Claus是卢卡斯的字母异位词！

见THIS LINK。

他的四卷本娱乐数学著作Récréations mathématiques Ⓣ（《数学娱乐》）（1882-94）已成为经典。

卢卡斯在一次宴会上的离奇事故中丧生，当时一只盘子掉落，碎片飞起划破了他的脸颊。几天后他死于丹毒。

Édouard Lucas was educated at the École Normale in Amiens. After this he worked at the Paris Observatory under Le Verrier.

During the Franco-Prussian War (1870-1871) Lucas served as an artillery officer. After the French were defeated, Lucas became professor of mathematics at the Lycée Saint Louis in Paris. He later became professor of mathematics at the Lycée Charlemagne, also in Paris.

Lucas is best known for his results in number theory: in particular he studied the Fibonacci sequence and the associated Lucas sequence is named after him. He gave the well-known formula for the Fibonacci numbers

The Lucas test for primes was refined by Lehmer in 1930. It works as follows. Define the sequence

Lucas showed that $S_{127}$ is divisible by $M_{127}$ thus showing that $M_{127}$ is prime. This was a extremely difficult calculation since $M_{127}$ is a big number and $S_{127}$ is unbelievably large. In fact

Lucas is also well known for his invention of the Tower of Hanoi puzzle and other mathematical recreations. The Tower of Hanoi puzzle appeared in 1883 under the name of M. Claus. Notice that Claus is an anagram of Lucas!

See THIS LINK.

His four volume work on recreational mathematics Récréations mathématiques Ⓣ (1882-94) has become a classic.

Lucas died as the result of a freak accident at a banquet when a plate was dropped and a piece flew up and cut his cheek. He died of erysipelas a few days later.