__NOTOC__ François Édouard Anatole Lucas (; 4 April 1842 – 3 October 1891) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, mathematical structure, structure, space, Mathematica ...

. Lucas is known for his study of the Fibonacci sequence. The related Lucas sequences and

Lucas number The Lucas sequence is an integer sequence named after the mathematician François Édouard Anatole Lucas (1842–1891), who studied both that sequence and the closely related Fibonacci sequence. Individual numbers in the Lucas sequence ar ...

s are named after him.

Biography

Lucas was born in

Amiens Amiens (English: or ; ; , or ) is a city and Communes of France, commune in northern France, located north of Paris and south-west of Lille. It is the capital of the Somme (department), Somme Departments of France, department in the region ...

and educated at the

École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

. He worked in the Paris Observatory and later became a professor of mathematics at the Lycée Saint Louis and the Lycée Charlemagne in

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

. Lucas served as an artillery officer in the French Army during the Franco-Prussian War of 1870–1871. In 1875, Lucas posed a challenge to prove that the only solution of the Diophantine equation :

\sum_^ n^2 = M^2\;

with ''N'' > 1 is when ''N'' = 24 and ''M'' = 70. This is known as the cannonball problem, since it can be visualized as the problem of taking a square arrangement of cannonballs on the ground and building a

square pyramid In geometry, a square pyramid is a Pyramid (geometry), pyramid with a square base and four triangles, having a total of five faces. If the Apex (geometry), apex of the pyramid is directly above the center of the square, it is a ''right square p ...

out of them. It was not until 1918 that a proof (using elliptic functions) was found for this remarkable fact, which has relevance to the bosonic string theory in 26 dimensions. More recently,

elementary proof In mathematics, an elementary proof is a mathematical proof that only uses basic techniques. More specifically, the term is used in number theory to refer to proofs that make no use of complex analysis. Historically, it was once thought that certain ...

s have been published. He devised methods for testing the primality of numbers. In 1857, at age 15, Lucas began testing the primality of 2¹²⁷ − 1, a number with 39 decimal digits, by hand, using Lucas sequences. In 1876, after 19 years of testing, he finally proved that 2¹²⁷ − 1 is prime; it remained the largest known

Mersenne prime In mathematics, a Mersenne prime is a prime number that is one less than a power of two. That is, it is a prime number of the form for some integer . They are named after Marin Mersenne, a French Minim friar, who studied them in the early 1 ...

for three-quarters of a century, and remains the largest prime number proved by hand. Later Derrick Henry Lehmer refined Lucas's primality tests and obtained the Lucas–Lehmer primality test. He worked on the development of the umbral calculus. Lucas is credited as the first to publish the Kempner function. Lucas was also interested in recreational mathematics. He found an elegant binary solution to the Baguenaudier puzzle. He also invented the Tower of Hanoi puzzle in 1883, which he marketed under the nickname ''N. Claus de Siam'', an

anagram An anagram is a word or phrase formed by rearranging the letters of a different word or phrase, typically using all the original letters exactly once. For example, the word ''anagram'' itself can be rearranged into the phrase "nag a ram"; which ...

of ''Lucas d'Amiens'', and published for the first time a description of the dots and boxes game in 1889. 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

sepsis Sepsis is a potentially life-threatening condition that arises when the body's response to infection causes injury to its own tissues and organs. This initial stage of sepsis is followed by suppression of the immune system. Common signs and s ...

, at 49 years old.

Works

* ''Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure'' (1877)
''Récréations scientifiques''
(1880)
''Théorie des nombres''
Tome Premier (1891)
''Récréations mathématiques''
(1894)
''L'arithmétique amusante''
(1895)

References

* *. *Harkin, D. “On the Mathematical Works of Francois-Édouard-Anatole Lucas, ''Enseignement mathematique'', 2nd ser., 3 (1957), 276–288.

External links

*
Scans of Lucas's original Tower of Hanoi puzzle in French, with translations
by Clark Kimberling
Édouard Lucas
{{DEFAULTSORT:Lucas, Edouard 1842 births 1891 deaths 19th-century French mathematicians French number theorists École Normale Supérieure alumni Fibonacci numbers Recreational mathematicians Mathematics popularizers Deaths from sepsis People from Amiens

Biography

Works

See also

References

External links