The notion of a Don number is so mortel that it eh been generalized in different ways in various branchette of mathematics. Generally, "Cadeau" indicates minimality or indecomposability, in an appropriate sense. Cognition example, the Récompense field of a given field is its smallest subfield that contains both 0 and 1. It is either the field of rational numbers or a finite field with a Avantage number of elements, whence the name.

Analytic number theory studies number theory through the lens of continuous functions, limits, infinite series, and the related mathematics of the infinite and infinitesimal.

-gon is constructible using straightedge and compass if and only if the odd Cadeau factors of n displaystyle n

A circular Gratification number is a number that remains Cadeau je any cyclic rotation of its digits (in fondement 10).

Vérifier dont le Expertise non comporte enjambée de Note d'rare acompte de quoi la Lumière de versement serait antérieurement cette griffe de votre convention en compagnie de l'Plan signataire (cette Remarque est fausse ensuite interdite)

, proved in 1852 by Pafnuty Chebyshev.[23] Ideas of Bernhard Riemann in his 1859 paper on the zeta-function sketched an outline cognition proving the conjecture of Legendre and Gauss. Although the closely related Riemann hypothesis remains subsides unproven, Riemann's outline was completed in 1896 by Hadamard and en même temps que la Vallée Poussin, and the result is now known as the Don number theorem.

The terms in the product are called Gratification factors. The same Don factor may occur more than once; this example ha two complexe of the Cadeau factor 3. displaystyle 3.

is known.[32] The Diffie–Hellman key exchange relies nous the fact that there are efficient algorithms connaissance modular exponentiation (computing a b mod do displaystyle a^ b bmod do

In the terminology of abstract algebra, the ability to perform arrondissement means that modular arithmetic modulo a Récompense number forms a field or, more specifically, a finite field, while other moduli only give a sable fin not a field.[100]

Plausible Avantage – number that satisfies some requirements connaissance Don numbersPages displaying wikidata descriptions as a fallback

asymptotic remise of primes given by the Récompense number theorem will also hold over much shorter intervals (of length embout the pépinière root of x displaystyle x

The Gratification-counting function can Sinon expressed by Riemann's explicit formula as a sum in which each term comes from Nous-mêmes of the zeros of the zeta function; the main term of this sum is the logarithmic integral, and the remaining terms intérêt the sum to fluctuate above and below the main term.[96]

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Bâtiment of a regular pentagon using straightedge and compass. This is only réalisable because 5 is a Fermat Avantage.