Édouard Lucas

Édouard Lucas (1842–1891) was a French mathematician whose work on number theory included tests for primality and studies of recurrence sequences.

Lucas sequence: A second-order recurrence sequence defined by two initial values and a recurrence relation. Lucas studied these sequences and used their divisibility properties in number theory.
Lucas primality test: A primality criterion that uses congruences involving a candidate integer and a suitable sequence or factorization. It names the family of tests most closely associated with Lucas’s work.
François Édouard Anatole Lucas: The full name of the French mathematician commonly known as Édouard Lucas. His full name appears in biographical and bibliographic records of Lucas’s work.
Lucas–Lehmer–Riesel test: A primality test for certain numbers of the form k·2^n − 1. It extends Lucas–Lehmer-style recurrence methods to a broader family of integers.
Lucas numbers: The sequence beginning 2, 1 in which each term is the sum of the two preceding terms. This companion to the Fibonacci sequence carries Lucas’s name and reflects his interest in recurrences.
Fibonacci sequence: The sequence beginning 0, 1 in which each term is the sum of the two preceding terms. Lucas investigated Fibonacci numbers and related recurrence sequences.
Lucas–Lehmer primality test: A recursive test that determines whether a Mersenne number is prime. This specialized test grew from Lucas’s methods and remains useful for Mersenne numbers.
Maurice Kraitchik: A Belgian mathematician and popularizer of recreational mathematics who wrote extensively on number theory. Kraitchik discussed Lucas’s methods and helped carry their mathematical history forward.
Lucas theorem: A theorem giving binomial coefficients modulo a prime in terms of the base-p digits of their arguments. This theorem bears Lucas’s name and supports computations of binomial coefficients modulo primes.
Lucas polynomial: A polynomial sequence satisfying a second-order recurrence and generalizing Lucas-type integer sequences. The broader algebraic theory of recurrence sequences preserves ideas associated with Lucas’s studies.

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