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Édouard Lucas was educated at the École Normale in Amiens. After this he worked at the Paris Observatory under Le Verrier.
During the FrancoPrussian War (18701871) 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 wellknown formula for the Fibonacci numbers
√5 f_{n} = ((1 + √5)/2)^{n}  ((1  √5)/2)^{n}.
Lucas also devised methods of testing primality, essentially those used today. In 1876 he used his methods to prove that the Mersenne number 2^{127}  1 is prime. This remains the largest prime number discovered without the aid of a computer.
The Lucas test for primes was refined by Lehmer in 1930. It works as follows. Define the sequence
S_{2} = 4, S_{3} = 14, S_{4} = 194, . . .
where for n >2, S_{n} is defined inductively by
S_{n} = S_{n1}^{2}  2.
The LucasLehmer test states that a Mersenne number M_{p} = 2^{p}  1, with p > 2, is prime if and only if M_{p} divides S_{p}.
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
M_{127} = 170141183460469231731687303715884105727
and Lucas was only able to perform the calculation since he showed that S_{127} is divisible by M_{127} without calculating S_{127}.
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! His four volume work on recreational mathematics Récréations mathématiques (188294) 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.
Article by: J J O'Connor and E F Robertson
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List of References (3 books/articles)
 
A Poster of Édouard Lucas
 Mathematicians born in the same country

Crossreferences in MacTutor
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JOC/EFR © December 1996 Copyright information 
School of Mathematics and Statistics University of St Andrews, Scotland  
The URL of this page is: http://wwwhistory.mcs.standrews.ac.uk/Biographies/Lucas.html 