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It is possible to deduce Wilson's theorem from a particular application of the Sylow theorems. Let p be a prime. It is immediate to deduce that the symmetric group S p {\displaystyle S_{p}} has exactly ( p − 1 ) ! {\displaystyle (p-1)!} elements of order p , namely the p -cycles C p {\displaystyle C_{p}} .
Bolyai–Gerwien theorem (discrete geometry) Bolzano's theorem (real analysis, calculus) Bolzano–Weierstrass theorem (real analysis, calculus) Bombieri's theorem (number theory) Bombieri–Friedlander–Iwaniec theorem (number theory) Bondareva–Shapley theorem ; Bondy's theorem (graph theory, combinatorics) Bondy–Chvátal theorem (graph ...
Clement's congruence-based theorem characterizes the twin primes pairs of the form (, +) through the following conditions: [()! +] ((+)), +P. A. Clement's original 1949 paper [2] provides a proof of this interesting elementary number theoretic criteria for twin primality based on Wilson's theorem.
Fermat's last theorem Fermat's last theorem, one of the most famous and difficult to prove theorems in number theory, states that for any integer n > 2, the equation a n + b n = c n has no positive integer solutions. Fermat's little theorem Fermat's little theorem field extension A field extension L/K is a pair of fields K and L such that K is ...
Pages in category "Theorems in geometry" The following 48 pages are in this category, out of 48 total. ... Bang's theorem on tetrahedra; Beckman–Quarles theorem;
In number theory, a Wilson prime is a prime number such that divides ()! +, where "!" denotes the factorial function; compare this with Wilson's theorem, which states that every prime divides ()! +. Both are named for 18th-century English mathematician John Wilson ; in 1770, Edward Waring credited the theorem to Wilson, [ 1 ] although it had ...
The Mandelbrot curves are defined by setting =, + = +, and then interpreting the set of points | | = in the complex plane as a curve in the real Cartesian plane of degree + in x and y. [19] Each curve n > 0 {\displaystyle n>0} is the mapping of an initial circle of radius 2 under p n {\displaystyle p_{n}} .
In geometry, a dissection problem is the problem of partitioning a geometric figure (such as a polytope or ball) into smaller pieces that may be rearranged into a new figure of equal content. In this context, the partitioning is called simply a dissection (of one polytope into another).