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Theory

The number theory problems about figures i. elizabeth. whole numbers or logical numbers (fractions).

Number theory is one of the earliest branches of pure math and among the largest. It is a branch of genuine mathematics concerning with the properties and integers. Arithmetic is additionally used to direct number theory. It is also referred to as higher math. The earliest geometric use of Diophantine equations could be tracked returning to the Sulba Sutras, that were written, between 8th and 6th hundreds of years BC. There are many number ideas described as employs:

Elementary Quantity theory

Inductive Number theory

Algebraic Amount theory

Geometric number theory

Combinational quantity theory

Computational number theory

FUNCTIONS

Amount theory is connected with bigger arithmetic therefore it is the research of homes of entire numbers. Primes and perfect factorization are important in amount theory. The functions in number theory are divisor function, Riemann Zeta function and totient function. The functions happen to be linked with Organic numbers, complete numbers, integers and realistic numbers. The functions are linked with irrational numbers. The study of irrational figures may be completed with Surd, Removal of Sq . roots of natural amounts, Logarithms and Mensuration.

Currently Number Theory functions have got 848 remedies, which are related with Prime Factorization Related functions and Other Features.

Prime Factorization Related Features

Factor Integer [n]70 Formulas

Division [n]sixty six Formulas

Perfect [n]83 Formulas

PrimePi [x]83 Formulas

Divisor Sigma [k, n]128 Formulas

Euler Phi [n]109 Formulas

Moebius Mu [n]seventy nine Formulas

Jacobi Symbol [n, m]tips Formulas

Carmichasel Lambda [n]63 Formulations

Digit Depend [n, b] 66 Formulas

Computational number theory

It is a analyze of success of methods for calculation of number-theoretic quantities. It is also considers integer quantities (for example school number) whose usual classification is no constructive, and real quantities (eg. The values of zeta functions) which must be computed with very high accuracy. Hence through this function terme conseillé both computer algebra and numerical analysis.

Combinational Amount Theory

This involves the number-theoretic study of objects, which happen naturally from counting or iteration. Also, it is study of many specific families of numbers like binomial rapport, the Fibonacci numbers, Bernoulli numbers, factorials, perfect squares, partition quantities etc . which can be obtained by simple repeat relations. The process is very simple to state conjectures in this area, which will often be understood with no particular mathematical training.

Integer factorization

Offered two significant prime figures, p and q, their particular product pq can easily be calculated. However , presented pq, the best known algorithms to recover l and queen require time greater than any polynomial in the length of s and queen.

Discrete logarithm

Let G be a group in which calculations are fairly efficient. In that case given g and d, computing gn is reasonably priced. However , for some groups G, computing and given g and gn, called the discrete logarithm, is tough. The commonly used groups happen to be

Discrete logarithms modulo l

Elliptic shape discrete logarithms

REFERENCE:

http://functions.wolfram.com/NumberTheoryFunctions/

Weil, Andre: “Number theory, An approach through history, Birkhauser Boston, Inc. Mass., 1984 ISBN-0-8176031410

Ore, Oystein, “Number theory as well as its history, Dover Publications, Incorporation., New York, 1988. 370 pp. ISBN 0-486-65620-9.

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