In mathematics, Wolstenholme's theorem states that for a prime number p ≥ 5, the congruence ( 2 p − 1 p − 1 ) ≡ 1 ( mod p 3 ) {\displaystyle {2p-1 \choose...

theory, a Wolstenholme prime is a special type of prime number satisfying a stronger version of Wolstenholme's theorem. Wolstenholme's theorem is a congruence...

England Wolstenholme prime, a prime number satisfying a certain congruence Wolstenholme number, a class of positive integers Wolstenholme's theorem, a congruence...

theory) Wilson's theorem (number theory) Wolstenholme's theorem (number theory) Zeckendorf's theorem (number theory) Zsigmondy's theorem (number theory)...

Joseph Wolstenholme, who proved Wolstenholme's theorem on modular relations of the generalized harmonic numbers. Weisstein, Eric W. "WolstenholmeNumber"...

{\displaystyle n>0} ) (sequence A001700 in the OEIS) is seen in Wolstenholme's theorem. By the Erdős squarefree conjecture, proved in 1996, no central...

conjecture: is 78,557 the lowest Sierpiński number? Does the converse of Wolstenholme's theorem hold for all natural numbers? Are all Euclid numbers square-free...

real influence upon successive generations of undergraduates; and "Wolstenholme's Problems" have proved a help and stimulus to many students. In 1869...

{\textstyle a_{n}} and b n {\textstyle b_{n}} . As a consequence of Wolstenholme's theorem, for any prime number p ≥ 5 {\displaystyle p\geq 5} the numerator...

than 4. Primes are central in number theory because of the fundamental theorem of arithmetic: every natural number greater than 1 is either a prime itself...

alternate statements characterizing primality are related to Wilson's theorem, or are restatements of this classical result given in terms of other special...

postulate is also called the Bertrand–Chebyshev theorem or Chebyshev's theorem. Chebyshev's theorem can also be stated as a relationship with π ( x )...

approximation Subfactorial Table of Newtonian series Taylor series Trinomial expansion Vandermonde's identity Wilson prime Wilson's theorem Wolstenholme prime...

_{k=1}^{n}k\right)^{2}.} This identity is sometimes called Nicomachus's theorem, after Nicomachus of Gerasa (c. 60 – c. 120 CE). Nicomachus, at the end...

than 1 that has no positive divisors other than 1 and itself. By Euclid's theorem, there are an infinite number of prime numbers. Subsets of the prime numbers...

1857 by showing that for the "first case" of Fermat's Last Theorem (see Sophie Germain's theorem) it is sufficient to establish that either (p, p − 3) or...

with primes, such as asymptotic behaviour according to the prime number theorem; also, a version of Goldbach's conjecture has been extended to them. There...

divides 2p − 1 − 1, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides 2p − 1 − 1. Wieferich primes...

unique up to the order of the factors. This fact is called the fundamental theorem of arithmetic. There are several known primality tests that can determine...

mathematical induction. From the second equation, we can deduce Goldbach's theorem (named after Christian Goldbach): no two Fermat numbers share a common...

prime Wilson prime Wolstenholme prime Woodall prime Prime pages Covering system Small set (combinatorics) Erdős–Ginzburg–Ziv theorem Polynomial method...

because of their close connection to perfect numbers: the Euclid–Euler theorem asserts a one-to-one correspondence between even perfect numbers and Mersenne...

Pedersen & te Riele (2003), Sándor & Crstici (2004)]. The Thābit ibn Qurrah theorem is a method for discovering amicable numbers invented in the 9th century...

square number, while other divisors come in pairs. Lagrange's four-square theorem states that any positive integer can be written as the sum of four or fewer...

{\displaystyle !} " denotes the factorial function; compare this with Wilson's theorem, which states that every prime p {\displaystyle p} divides ( p − 1 ) !...

where the strict converse of Fermat's Little Theorem does not hold. This fact precludes the use of that theorem as an absolute test of primality. The Carmichael...

after the ancient Greek mathematician Euclid, in connection with Euclid's theorem that there are infinitely many prime numbers. For example, the first three...

important class of pseudoprimes that come from Fermat's little theorem. Fermat's little theorem states that if p {\displaystyle p} is prime and a {\displaystyle...

Expressible via specific sums Nonhypotenuse Polite Practical Primary pseudoperfect Ulam Wolstenholme...

other fourth powers (the n = 4 case of Fermat's Last Theorem; see Fermat's right triangle theorem). Euler conjectured that a fourth power cannot be written...