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In algebra and number theory, Wilson's theorem states that a natural number n > 1 is a prime number if and only if the product of all the positive integers less than ...
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 ...
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.
Because the set of primes is a computably enumerable set, by Matiyasevich's theorem, it can be obtained from a system of Diophantine equations. Jones et al. (1976) found an explicit set of 14 Diophantine equations in 26 variables, such that a given number k + 2 is prime if and only if that system has a solution in nonnegative integers: [7]
Pages in category "Theorems about prime numbers" ... Wilson's theorem; Wolstenholme's theorem This page was last edited on 22 March 2013, at 11:36 (UTC). ...
Around 1000 AD, the Islamic mathematician Ibn al-Haytham (Alhazen) found Wilson's theorem, characterizing the prime numbers as the numbers that evenly divide ()! +. He also conjectured that all even perfect numbers come from Euclid's construction using Mersenne primes, but was unable to prove it. [18]
Linear congruence theorem; Method of successive substitution; Chinese remainder theorem; Fermat's little theorem. Proofs of Fermat's little theorem; Fermat quotient; Euler's totient function. Noncototient; Nontotient; Euler's theorem; Wilson's theorem; Primitive root modulo n. Multiplicative order; Discrete logarithm; Quadratic residue. Euler's ...
Wiener–Ikehara theorem (number theory) Wigner–Eckart theorem (Clebsch–Gordan coefficients) Wilkie's theorem (model theory) Wilson's theorem (number theory) Witt's theorem (quadratic forms) Wold's theorem ; Wolstenholme's theorem (number theory)