François Edouard Anatole Lucas (April 4th 1842 - October 3rd 1891) is a French mathematician.

## Biography

Born with Amiens, Edouard Lucas makes his studies in Amiens with the Louis-Thuillier college, then it made its preparation with Douai to integrate the Teacher training school. At that time, it met Pasteur which rather directed it towards the Teacher training school than towards Polytechnique.

At its exit, he works with the Observatoire of Paris under the direction of the Glassmaker. The two men get along badly.

During the War of 1870, it is useful as an officer in artillery.

He becomes professor of mathematics to the Lycée Saint-Louis then with the Lycée Charlemagne.

Edouard Lucas dies in Paris following an unhappy accident. At the time of a banquet, it is wounded with the cheek by the glare of a dish which had just fallen to ground. He died of erysipelas a few days after (Dermite due to a Streptocoque).

## Work mathematical

Edouard Lucas is well-known for his results in Théorie of the numbers, in particular for the study of the Suite of Fibonacci as well as continuation associated known as with Lucas .

Edouard Lucas invented the test of primality which is still used usually nowadays. In 1876, it used its method to show that the number of Mersenne M127 is first. This number remains the greatest prime number identified without the assistance of a computer.

The test of primality of Lucas is updated in 1930 by Lehmer which defines it as follows. One defines a succession of Sn entireties by the formula

S2 = 4, Sn = (Sn-1) ² - 2 for n>2.
The first terms are
S2 = 4, S3 = 14, S4 = 194,…

The Test of primality of Lucas-Lehmer for the numbers of Mersenne stipulates that a number of Mersenne Mp = 2p − 1, with p>2, is first if and only if Sp is divisible by Mp.

Edouard Lucas showed that S127 was divisible by M127, which thus involves that M127 is first. The thing was extremely delicate, knowing that M127 is very large and that S127 is enormous. Edouard Lucas made the demonstration without calculating S127 (for M3217, a demonstration is obtained in 1957).

M127 = 170141183460469231731687303715884105727

Edouard Lucas is also known for the invention of some plays like the Baguenaudier and the Tours of Hanoï, the name of the so-called importer of the play was NR. Claus of Siam (anagram of Lucas of Amiens). To note that the minimal number of blows to move a tower is a number of Mersenne (eight discs is 255 blows). It also designs calculating machines, of which the Réglettes of Genaille-Lucas.

It publishes several books on mathematics and the four famous volumes of the mathematical recreations, whose two last will be published in posthumous title (1882 - 1894).

## External bond

Edouard Lucas

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