Number theory

The number possible action concerns about be i.e. whole numbers or rational numbers (fractions). weigh guess is one of the oldest branches of pure mathematics and one of the largest. It is a branch of pure mathematics concerning with the properties and integers. Arithmetic is similarly used to confab number theory. It is also called higher arithmetical. The earliest geometric use of Diophantine equations bathroom be tracked back to the Sulba Sutras, which were written, between 8th and 6th centuries BC. at that place be various number theories described as followsElementary minute theory Analytic Number theory Algebraic Number theory Geometric number theory Combinational number theory computational number theory FUNCTIONSNumber theory is connected with higher arithmetic hence it is the study of properties of whole numbers. meridians and prime factorization are authorized in number theory. The functions in number theory are gene function, Riemann Zeta function and totient function. The functions are linked with Natural numbers, whole numbers, integers and rational numbers. The functions are also linked with irrational numbers. The study of irrational numbers may be done with Surd, Extraction of Square roots of natural numbers, Logarithms and Mensuration.At present Number Theory functions have 848 formulas, which are related with Prime computeization Related functions and Other Functions.Prime Factorization Related FunctionsFactor whole number n 70 FormulasDivision n 66 FormulasPrime n 83 FormulasPrimePi x 83 FormulasDivisor Sigma k,n 128 FormulasEuler Phi n 109 FormulasMoebius Mu n 79 FormulasJacobi Symbol n,m 101 FormulasCarmichasel Lambda n 63 FormulasDigit number n, b 66 FormulasComputational number theory It is a study of posture of algorithms for computation of number-theoretic quantities. It is also considers integer quantities (for example class number) whose usual description is non constructive, and real quantities (eg. The values of z eta functions) which must be computed with very high precision. therefrom in this function overlaps both computer algebra and numerical analysis.Combinational Number Theory It involves the number-theoretic study of objects, which arise naturally from counting or iteration. It is also study of many specific families of numbers like binomial coefficients, the Fibonacci numbers, Bernoulli numbers, factorials, consummate squares, partition numbers etc. which puke be obtained by wide-eyed recurrence relations. The method is very easy to state conjectures in this area, which can often be understood without any particular mathematical training.Integer factorization Given two large prime numbers, p and q, their output pq can easily be computed. However, given over pq, the best known algorithms to detect p and q require time greater than any polynomial in the length of p and q.distinct logarithm Let G be a group in which computations are reasonably efficient. Then given g and n, compu ting gn is not too expensive. However, for some groups G, computing n given g and gn, called the discrete logarithm, is difficult. The commonly used groups areDiscrete logarithms modulo p Elliptic curve discrete logarithms REFERENCEhttp//functions.wolfram.com/NumberTheoryFunctions/ Weil, Andre Number theory, An come up through history, Birkhauser Boston, Inc. Mass., 1984 ISBN-0-8176031410 Ore, Oystein, Number theory and its history, Dover Publications, Inc., New York, 1988. 370 pp. ISBN 0-486-65620-9.