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Dirichlet's theorem on arithmetic progressions and Prime number

Shortcuts: Differences, Similarities, Jaccard Similarity Coefficient, References.

Difference between Dirichlet's theorem on arithmetic progressions and Prime number

Dirichlet's theorem on arithmetic progressions vs. Prime number

In number theory, Dirichlet's theorem, also called the Dirichlet prime number theorem, states that for any two positive coprime integers a and d, there are infinitely many primes of the form a + nd, where n is a non-negative integer. A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

Similarities between Dirichlet's theorem on arithmetic progressions and Prime number

Dirichlet's theorem on arithmetic progressions and Prime number have 19 things in common (in Unionpedia): Algebraic number theory, Analytic number theory, Annals of Mathematics, Arithmetic progression, Chebotarev's density theorem, Coprime integers, Euclid's theorem, Euler's totient function, Gaussian integer, Green–Tao theorem, Landau's problems, Modular arithmetic, Multiplicative inverse, Number theory, Prime number theorem, Prime Pages, Quadratic reciprocity, Riemann zeta function, Springer Science+Business Media.

Algebraic number theory

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.

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Analytic number theory

In mathematics, analytic number theory is a branch of number theory that uses methods from mathematical analysis to solve problems about the integers.

Analytic number theory and Dirichlet's theorem on arithmetic progressions · Analytic number theory and Prime number · See more »

Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

Annals of Mathematics and Dirichlet's theorem on arithmetic progressions · Annals of Mathematics and Prime number · See more »

Arithmetic progression

In mathematics, an arithmetic progression (AP) or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant.

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Chebotarev's density theorem

Chebotarev's density theorem in algebraic number theory describes statistically the splitting of primes in a given Galois extension K of the field \mathbb of rational numbers.

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Coprime integers

In number theory, two integers and are said to be relatively prime, mutually prime, or coprime (also written co-prime) if the only positive integer (factor) that divides both of them is 1.

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Euclid's theorem

Euclid's theorem is a fundamental statement in number theory that asserts that there are infinitely many prime numbers.

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Euler's totient function

In number theory, Euler's totient function counts the positive integers up to a given integer that are relatively prime to.

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Gaussian integer

In number theory, a Gaussian integer is a complex number whose real and imaginary parts are both integers.

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Green–Tao theorem

In number theory, the Green–Tao theorem, proved by Ben Green and Terence Tao in 2004, states that the sequence of prime numbers contains arbitrarily long arithmetic progressions.

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Landau's problems

At the 1912 International Congress of Mathematicians, Edmund Landau listed four basic problems about primes.

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Modular arithmetic

In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" upon reaching a certain value—the modulus (plural moduli).

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Multiplicative inverse

In mathematics, a multiplicative inverse or reciprocal for a number x, denoted by 1/x or x−1, is a number which when multiplied by x yields the multiplicative identity, 1.

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Number theory

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.

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Prime number theorem

In number theory, the prime number theorem (PNT) describes the asymptotic distribution of the prime numbers among the positive integers.

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Prime Pages

The Prime Pages is a website about prime numbers maintained by Chris Caldwell at the University of Tennessee at Martin.

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Quadratic reciprocity

In number theory, the law of quadratic reciprocity is a theorem about modular arithmetic that gives conditions for the solvability of quadratic equations modulo prime numbers.

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Riemann zeta function

The Riemann zeta function or Euler–Riemann zeta function,, is a function of a complex variable s that analytically continues the sum of the Dirichlet series which converges when the real part of is greater than 1.

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Springer Science+Business Media

Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

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The list above answers the following questions

Dirichlet's theorem on arithmetic progressions and Prime number Comparison

Dirichlet's theorem on arithmetic progressions has 42 relations, while Prime number has 340. As they have in common 19, the Jaccard index is 4.97% = 19 / (42 + 340).

References

This article shows the relationship between Dirichlet's theorem on arithmetic progressions and Prime number. To access each article from which the information was extracted, please visit:

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