base p expansions of the integers m and n. Lucas's theorem first appeared in 1878 in papers by Édouard Lucas. For non-negative integers m and n and a prime...

_{i=1}^{k}S_{p}(m_{i})\right)-S_{p}(n)\right).} Lucas's theorem Mihet, Dorel (December 2010). "Legendre's and Kummer's Theorems Again". Resonance. 15 (12): 1111–1121...

In complex analysis, a branch of mathematics, the Gauss–Lucas theorem gives a geometric relation between the roots of a polynomial P and the roots of...

Glaisher[citation needed]) and is inspired by Lucas's theorem. No known composite numbers satisfy Wolstenholme's theorem and it is conjectured that there are none...

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...

Lindemann–Weierstrass theorem (transcendental number theory) Linnik's theorem (number theory) Lochs's theorem (number theory) Lucas's theorem (number theory)...

In calculus, Rolle's theorem or Rolle's lemma essentially states that any real-valued differentiable function that attains equal values at two distinct...

Marden's theorem, a refinement of Gauss–Lucas theorem for polynomials of degree three Sendov's conjecture, a conjectured refinement of Gauss-Lucas theorem zero...

In algebra, the rational root theorem (or rational root test, rational zero theorem, rational zero test or p/q theorem) states a constraint on rational...

of p, that is the sum of the bitsize of its coefficients. The Gauss–Lucas theorem states that the convex hull of the roots of a polynomial contains the...

derivative by a variant of Euclid's algorithm for polynomials. Sturm's theorem expresses the number of distinct real roots of p located in an interval...

necessarily distinct) complex roots r1, r2, ..., rn by the fundamental theorem of algebra. Vieta's formulas relate the polynomial coefficients to signed...

a triangle, and the Gauss–Lucas theorem states that the roots of its derivative lie within this triangle. Marden's theorem states their location within...

certificates are based on Lucas's theorem, Atkin–Goldwasser–Kilian–Morain certificates are based on the following theorem of Goldwasser and Kilian (lemma...

Gödel's incompleteness theorems are two theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories...

Riemann–Roch theorem. Argument principle Control theory § Stability Filter design Filter (signal processing) Gauss–Lucas theorem Hurwitz's theorem (complex...

Marguerite's Theorem (French: Le Théorème de Marguerite) is 2023 French-Swiss drama film co-written and directed by Anna Novion [fr]. It is about a female...

Gauss–Bodenmiller theorem – described on website of University of Crete Gauss–Bolyai–Lobachevsky space, a hyperbolic geometry Gauss–Bonnet theorem, a theorem about...

roots. Convex hulls and polynomials also come together in the Gauss–Lucas theorem, according to which the roots of the derivative of a polynomial all...

integer coefficients of ⁠ f . {\displaystyle f.} ⁠ The analogue of Lucas's theorem for multinomial coefficients p ! i ! j ! k ! {\displaystyle {\frac...

Tarski's undefinability theorem, stated and proved by Alfred Tarski in 1933, is an important limitative result in mathematical logic, the foundations...

In number theory, Fermat's little theorem states that if p is a prime number, then for any integer a, the number ap − a is an integer multiple of p. In...

The Zero Theorem is a 2013 science fiction film directed by Terry Gilliam, starring Christoph Waltz, David Thewlis, Mélanie Thierry and Lucas Hedges. Written...

Banach fixed-point theorem (also known as the contraction mapping theorem or contractive mapping theorem or Banach–Caccioppoli theorem) is an important...

series of .pdf files on Lucas's website (below). Also available as Reason and Reality: An Essay in Metaphysics by J. R. Lucas (494 pages, December 2009):...

primes. Double exponential function Lucas' theorem Mersenne prime Pierpont prime Primality test Proth's theorem Pseudoprime Sierpiński number Sylvester's...

roots in any interval. This is the basic idea of Budan's theorem and the Budan–Fourier theorem. Repeated division of an interval in two results in a set...

distance no more than 1 from at least one critical point. The Gauss–Lucas theorem says that all of the critical points lie within the convex hull of the...

point because it is not included in the function's domain. By the Gauss–Lucas theorem, all of a polynomial function's critical points in the complex plane...

"Minds, Machines and Gödel" is J. R. Lucas's 1959 philosophical paper in which he argues that a human mathematician cannot be accurately represented by...