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Number theory and P-adic number

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

Difference between Number theory and P-adic number

Number theory vs. P-adic number

Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers. In mathematics, the -adic number system for any prime number extends the ordinary arithmetic of the rational numbers in a different way from the extension of the rational number system to the real and complex number systems.

Similarities between Number theory and P-adic number

Number theory and P-adic number have 18 things in common (in Unionpedia): Algebraic number field, Divisor, E (mathematical constant), Ernst Kummer, Fermat's Last Theorem, Galois group, Graduate Texts in Mathematics, Integer, Number, Power series, Prime ideal, Prime number, Quadratic form, Rational number, Real number, Ring (mathematics), Solvable group, Valuation (algebra).

Algebraic number field

In mathematics, an algebraic number field (or simply number field) F is a finite degree (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector space over Q. The study of algebraic number fields, and, more generally, of algebraic extensions of the field of rational numbers, is the central topic of algebraic number theory.

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Divisor

In mathematics, a divisor of an integer n, also called a factor of n, is an integer m that may be multiplied by some integer to produce n. In this case, one also says that n is a multiple of m. An integer n is divisible by another integer m if m is a divisor of n; this implies dividing n by m leaves no remainder.

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E (mathematical constant)

The number is a mathematical constant, approximately equal to 2.71828, which appears in many different settings throughout mathematics.

E (mathematical constant) and Number theory · E (mathematical constant) and P-adic number · See more »

Ernst Kummer

Ernst Eduard Kummer (29 January 1810 – 14 May 1893) was a German mathematician.

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Fermat's Last Theorem

In number theory, Fermat's Last Theorem (sometimes called Fermat's conjecture, especially in older texts) states that no three positive integers,, and satisfy the equation for any integer value of greater than 2.

Fermat's Last Theorem and Number theory · Fermat's Last Theorem and P-adic number · See more »

Galois group

In mathematics, more specifically in the area of abstract algebra known as Galois theory, the Galois group of a certain type of field extension is a specific group associated with the field extension.

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Graduate Texts in Mathematics

Graduate Texts in Mathematics (GTM) (ISSN 0072-5285) is a series of graduate-level textbooks in mathematics published by Springer-Verlag.

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Integer

An integer (from the Latin ''integer'' meaning "whole")Integer 's first literal meaning in Latin is "untouched", from in ("not") plus tangere ("to touch").

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Number

A number is a mathematical object used to count, measure and also label.

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Power series

In mathematics, a power series (in one variable) is an infinite series of the form where an represents the coefficient of the nth term and c is a constant.

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Prime ideal

In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.

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Prime number

A prime number (or a prime) is a natural number greater than 1 that cannot be formed by multiplying two smaller natural numbers.

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Quadratic form

In mathematics, a quadratic form is a homogeneous polynomial of degree two in a number of variables.

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Rational number

In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.

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Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

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Ring (mathematics)

In mathematics, a ring is one of the fundamental algebraic structures used in abstract algebra.

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Solvable group

In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions.

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Valuation (algebra)

In algebra (in particular in algebraic geometry or algebraic number theory), a valuation is a function on a field that provides a measure of size or multiplicity of elements of the field.

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The list above answers the following questions

Number theory and P-adic number Comparison

Number theory has 216 relations, while P-adic number has 135. As they have in common 18, the Jaccard index is 5.13% = 18 / (216 + 135).

References

This article shows the relationship between Number theory and P-adic number. To access each article from which the information was extracted, please visit:

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