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41 relations: Abraham Adrian Albert, Bernard Frénicle de Bessy, Cambridge University Press, Carmichael function, Carmichael number, Carmichael's theorem, Converse (logic), Coprime integers, Cut-the-Knot, D. C. Heath and Company, Euler's theorem, Euler's totient function, Extended Euclidean algorithm, Fermat primality test, Fermat quotient, Fermat's Last Theorem, Finite field, Frobenius endomorphism, Geometric progression, Gottfried Wilhelm Leibniz, Integer, Kurt Hensel, Lagrange's theorem (group theory), Leonhard Euler, Lucas–Lehmer primality test, Miller–Rabin primality test, Modular arithmetic, Modular exponentiation, Modular multiplicative inverse, Number theory, P-derivation, Paulo Ribenboim, Pierre de Fermat, Pierre Frédéric Sarrus, Prentice Hall, Primality test, Prime number, Pseudoprime, Public-key cryptography, RSA (cryptosystem), Table of congruences.
Abraham Adrian Albert
Abraham Adrian Albert (November 9, 1905 – June 6, 1972) was an American mathematician.
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Bernard Frénicle de Bessy
Bernard Frénicle de Bessy (c. 1604 – 1674), was a French mathematician born in Paris, who wrote numerous mathematical papers, mainly in number theory and combinatorics.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Carmichael function
In number theory, the Carmichael function associates to every positive integer n a positive integer \lambda(n), defined as the smallest positive integer m such that (Dropping the phrase "between 1 and n" leads to an equivalent definition.) In algebraic terms, \lambda(n) equals the exponent of the multiplicative group of integers modulo ''n''.
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Carmichael number
In number theory, a Carmichael number is a composite number n which satisfies the modular arithmetic congruence relation: for all integers b which are relatively prime to n. They are named for Robert Carmichael.
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Carmichael's theorem
In number theory, Carmichael's theorem, named after the American mathematician R.D. Carmichael, states that, for any nondegenerate Lucas sequence of the first kind Un(P,Q) with relatively prime parameters P, Q and positive discriminant, an element Un with n ≠ 1, 2, 6 has at least one prime divisor that does not divide any earlier one except the 12th Fibonacci number F(12).
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Converse (logic)
In logic, the converse of a categorical or implicational statement is the result of reversing its two parts.
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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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Cut-the-Knot
Cut-the-knot is a free, advertisement-funded educational website maintained by Alexander Bogomolny and devoted to popular exposition of many topics in mathematics.
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D. C. Heath and Company
D.C. Heath and Company was an American publishing company located at 125 Spring Street in Lexington, Massachusetts, specializing in textbooks.
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Euler's theorem
In number theory, Euler's theorem (also known as the Fermat–Euler theorem or Euler's totient theorem) states that if n and a are coprime positive integers, then where \varphi(n) is Euler's totient function.
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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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Extended Euclidean algorithm
In arithmetic and computer programming, the extended Euclidean algorithm is an extension to the Euclidean algorithm, and computes, in addition to the greatest common divisor of integers a and b, also the coefficients of Bézout's identity, which are integers x and y such that This is a certifying algorithm, because the gcd is the only number that can simultaneously satisfy this equation and divide the inputs.
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Fermat primality test
The Fermat primality test is a probabilistic test to determine whether a number is a probable prime.
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Fermat quotient
In number theory, the Fermat quotient of an integer a with respect to an odd prime p is defined as: at The Prime Glossary or This article is about the former.
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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.
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Finite field
In mathematics, a finite field or Galois field (so-named in honor of Évariste Galois) is a field that contains a finite number of elements.
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Frobenius endomorphism
In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class which includes finite fields.
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Geometric progression
In mathematics, a geometric progression, also known as a geometric sequence, is a sequence of numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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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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Kurt Hensel
Kurt Wilhelm Sebastian Hensel (29 December 1861 – 1 June 1941) was a German mathematician born in Königsberg.
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Lagrange's theorem (group theory)
Lagrange's theorem, in the mathematics of group theory, states that for any finite group G, the order (number of elements) of every subgroup H of G divides the order of G. The theorem is named after Joseph-Louis Lagrange.
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Leonhard Euler
Leonhard Euler (Swiss Standard German:; German Standard German:; 15 April 170718 September 1783) was a Swiss mathematician, physicist, astronomer, logician and engineer, who made important and influential discoveries in many branches of mathematics, such as infinitesimal calculus and graph theory, while also making pioneering contributions to several branches such as topology and analytic number theory.
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Lucas–Lehmer primality test
In mathematics, the Lucas–Lehmer test (LLT) is a primality test for Mersenne numbers.
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Miller–Rabin primality test
The Miller–Rabin primality test or Rabin–Miller primality test is a primality test: an algorithm which determines whether a given number is prime, similar to the Fermat primality test and the Solovay–Strassen primality test.
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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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Modular exponentiation
Modular exponentiation is a type of exponentiation performed over a modulus.
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Modular multiplicative inverse
In mathematics, in particular the area of number theory, a modular multiplicative inverse of an integer is an integer such that the product is congruent to 1 with respect to the modulus.
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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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P-derivation
In mathematics, more specifically differential algebra, a p-derivation (for p a prime number) on a ring R, is a mapping from R to R that satisfies certain conditions outlined directly below.
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Paulo Ribenboim
Paulo Ribenboim (born March 13, 1928) is a Brazilian-Canadian mathematician who specializes in number theory.
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Pierre de Fermat
Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
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Pierre Frédéric Sarrus
Pierre Frédéric Sarrus (10 March 1798, Saint-Affrique – 20 November 1861) was a French mathematician.
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Prentice Hall
Prentice Hall is a major educational publisher owned by Pearson plc.
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Primality test
A primality test is an algorithm for determining whether an input number is prime.
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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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Pseudoprime
A pseudoprime is a probable prime (an integer that shares a property common to all prime numbers) that is not actually prime.
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Public-key cryptography
Public-key cryptography, or asymmetric cryptography, is any cryptographic system that uses pairs of keys: public keys which may be disseminated widely, and private keys which are known only to the owner.
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RSA (cryptosystem)
RSA (Rivest–Shamir–Adleman) is one of the first public-key cryptosystems and is widely used for secure data transmission.
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Table of congruences
In mathematics, a congruence is an equivalence relation on the integers.
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Fermat lesser theorem, Fermat little theorem, Fermat simple theorem, Fermat's Little Theorem, Fermat's Little Theorem Converse, Fermat's Little theorem, Fermat's lesser theorem, Fermat's simple theorem, Fermats little theorem, Fermats little theorom, Little Fermat theorem.
References
[1] https://en.wikipedia.org/wiki/Fermat's_little_theorem
