Édouard Lucas: Difference between revisions

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François Édouard Anatole Lucas (April 4, 1842 in Amiens - October 3, 1891) was a French mathematician. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequence is named after him. He gave a formula for finding the n^th term of the Fibonacci sequence.

Lucas was educated at the École Normale Supérieure. He worked in the Paris observatory and later became a professor of mathematics in Paris. In the meantime he served in the army.

Lucas posed a challenge to prove that the only solution of the Diophantine equation:

\sum _{n=1}^{N}n^{2}=M^{2}\;

with N > 1 is when N=24 and M=70. It was not until 1918 that a proof (using hyperelliptic functions) was found for this remarkable fact, which has relevance to the bosonic string theory in 26-dimensions [1].

He devised methods for testing the primality of numbers. In late 1856, at age 14, Lucas began testing the primality of 2¹²⁷-1 by hand, using Lucas Sequences. In 1876, after 19 years of testing, he finally proved that 2¹²⁷−1 was prime; this would remain the largest known Mersenne prime for three-quarters of a century. This may stand forever as the largest prime number proven by hand. Later Derrick Henry Lehmer refined his work and obtained the Lucas-Lehmer test for Mersenne numbers.

He worked on the development of the umbral calculus.

Lucas was also interested in recreational mathematics; He discovered an elegant binary solution to the Baguenaudier puzzle. He also more notably invented the Tower of Hanoi puzzle, which he marketed under the nickname N. Claus de Siam, an anagram of Lucas d'Amiens.

Lucas died in unusual circumstances. At the banquet of the annual congress of the Association 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 by septicemia.

External links

O'Connor, John J.; Robertson, Edmund F., "Édouard Lucas", MacTutor History of Mathematics Archive, University of St Andrews
Scans of Lucas's original Tower of Hanoi puzzle in French, with translations
Édouard Lucas, by Clark Kimberling
Édouard Lucas, the official web-site.

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 with ''N'' > 1 is when ''N''=24 and ''M''=70. It was not until 1918 that a proof (using [[hyperelliptic function]]s) was found for this remarkable fact, which has relevance to the bosonic [[string theory]] in 26-dimensions [http://math.ucr.edu/home/baez/week95.html].
-He devised methods for testing the [[prime number|primality]] of numbers. He proved in 1876 that 2<sup>127</sup>−1 was prime; this would remain the largest known [[Mersenne prime]] for three-quarters of a century. Later [[Derrick Henry Lehmer]] refined his work and obtained the [[Lucas-Lehmer test for Mersenne numbers]].
+He devised methods for testing the [[prime number|primality]] of numbers. In late 1856, at age 14, Lucas began testing the primality of 2<sup>127</sup>-1 by hand, using Lucas Sequences. In 1876, after 19 years of testing, he finally proved that 2<sup>127</sup>−1 was prime; this would remain the largest known [[Mersenne prime]] for three-quarters of a century. This may stand forever as the largest prime number proven by hand. Later [[Derrick Henry Lehmer]] refined his work and obtained the [[Lucas-Lehmer test for Mersenne numbers]].
 He worked on the development of the [[umbral calculus]].

Revision as of 16:09, 6 July 2007

See also

External links