# Mathematician:Édouard Lucas

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## Contents

## Mathematician

French mathematician best known for his study of the Fibonacci numbers. As a result of his researches, discovered what are now known as the Lucas numbers.

In $1876$, proved that the Mersenne number $M_{127}$ is prime, and discovered that $M_{67}$ is actually composite.

Discovered a method of determining the primality of a Mersenne number. This technique was refined in the $1930$s by Derrick Henry Lehmer and became known as the Lucas-Lehmer Test.

## Nationality

French

## History

- Born: April 4, 1842
- Died: October 3, 1891

## Theorems and Definitions

- Lucas Numbers
- Lucas-Lehmer Test for Mersenne primes (with Derrick Henry Lehmer)
- Lucas Prime
- Gauss-Lucas Theorem (with Carl Friedrich Gauss)
- Lucas' Theorem
- Pell-Lucas Numbers (with John Pell)
- Lucas-Carmichael Number (with Robert Daniel Carmichael)

- Fibonomial Coefficient (named for Leonardo Fibonacci)

Results named for **Édouard Lucas** can be found here.

Definitions of concepts named for **Édouard Lucas** can be found here.

## Publications

- 1877:
*Recherches Sur Plusieurs Ouvrages De Léonard De Pise Et Sur Diverses Questions D’Arithmétique Supérieure* - 1878:
*Théorie des Fonctions Numériques Simplement Périodiques*(*Amer. J. Math.***Vol. 1**,*no. 2*: 184 – 196) www.jstor.org/stable/2369308 - 1878:
*Théorie des Fonctions Numériques Simplement Périodiques*(*Amer. J. Math.***Vol. 1**,*no. 3*: 197 – 240) www.jstor.org/stable/2369311 - 1878:
*Théorie des Fonctions Numériques Simplement Périodiques*(*Amer. J. Math.***Vol. 1**,*no. 4*: 289 – 321) www.jstor.org/stable/2369373 - 1883: The Tower of Hanoi puzzle
- 1891:
*Théorie des nombres, Tome Premiere* - 1894:
*Récréations mathématiques* - 1895:
*L'arithmétique amusante*

## Also known as

Full name: **François Édouard Anatole Lucas**.

Published his famous Tower of Hanoi puzzle under the name **M. Claus**.

## Sources

- 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1986: David Wells:
*Curious and Interesting Numbers*... (previous) ... (next): $11$ - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): A List of Mathematicians in Chronological Sequence - 1997: David Wells:
*Curious and Interesting Numbers*(2nd ed.) ... (previous) ... (next): $11$