Édouard Lucas | |
|---|---|
 | |
| Born | (1842-04-04)4 April 1842 |
| Died | 3 October 1891(1891-10-03) (aged 49) |
| Alma mater | École Normale Supérieure |
| Known for | Lucas number Lucas sequence Lucas primality test Lucas–Lehmer primality test Lucas prime Lucas's theorem Genaille–Lucas rulers Ménage problem Tower of Hanoi |
| Scientific career | |
| Fields | Mathematics |
François Édouard Anatole Lucas (French pronunciation:[fʁɑ̃swaedwaʁanatɔllykɑ]; 4 April 1842 – 3 October 1891) was a Frenchmathematician. Lucas is known for his study of theFibonacci sequence. The relatedLucas sequences andLucas numbers are named after him.
Lucas was born inAmiens and educated at theÉcole Normale Supérieure.[1] He worked in theParis Observatory and later became a professor of mathematics at the Lycée Saint Louis and the Lycée Charlemagne inParis.[1]
Lucas served as an artillery officer in the French Army during the Franco-Prussian War of 1870–1871.[1]
In 1875, Lucas posed a challenge toprove that the only solution of theDiophantine equation
withN > 1 is whenN = 24 andM = 70. This is known as thecannonball problem, since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building asquare pyramid out of them. It was not until 1918 that a proof (usingelliptic functions) was found for this remarkable fact, which has relevance to thebosonic string theory in 26 dimensions.[2] More recently,elementary proofs have been published.[3][4]
He devised methods for testing theprimality of numbers. In 1857, at age 15, Lucas began testing the primality of 2127 − 1, a number with 39 decimal digits, by hand, usingLucas sequences. In 1876, after 19 years of testing,[5] he finally proved that 2127 − 1 is prime; it remained the largest knownMersenne prime for three-quarters of a century, and remains the largest prime number proved by hand. LaterDerrick Henry Lehmer refined Lucas'sprimality tests and obtained theLucas–Lehmer primality test.
He worked on the development of theumbral calculus.
Lucas is credited as the first to publish theKempner function.[6]
Lucas was also interested inrecreational mathematics. He found an elegantbinary solution to theBaguenaudier puzzle.[7] He also invented theTower of Hanoi puzzle in 1883, which he marketed under the nicknameN. Claus de Siam, ananagram ofLucas d'Amiens, and published for the first time a description of thedots and boxes game in 1889.
At the banquet of the annual congress of theAssociation française pour l'avancement des sciences, a waiter dropped some crockery and a piece of broken plate cut Lucas on the cheek. He died a few days later of a severe skin inflammation, probably caused bysepsis, at 49 years old.
