Number theory

Fermat quotient

In number theory, the Fermat quotient of an integer a with respect to an odd prime p is defined as or . This article is about the former; for the latter see p-derivation. The quotient is named after Pierre de Fermat. If the base a is coprime to the exponent p then Fermat's little theorem says that qp(a) will be an integer. If the base a is also a generator of the multiplicative group of integers modulo p, then qp(a) will be a cyclic number, and p will be a full reptend prime. (Wikipedia).

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PreCalculus | Finding the difference quotient: Example 3

We present a few examples of calculating the difference quotient. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/

From playlist PreCalculus

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Ex 2: The Difference Quotient (Quadratic Function)

This video provides an example of how to find the difference quotient for a quadratic function. Site: http://mathispower4u.com

From playlist Determining Function Values

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Theory of numbers: Fermat's theorem

This lecture is part of an online undergraduate course on the theory of numbers. We prove Fermat's theorem a^p = a mod p. We then define the order of a number mod p and use Fermat's theorem to show the order of a divides p-1. We apply this to testing some Fermat and Mersenne numbers to se

From playlist Theory of numbers

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Prime Factorization - Fermat Algorithm

Description and example of getting the prime factors of a number using the Fermat algorithm. Questions? Feel free to post them in the comments and I'll do my best to answer!

From playlist Cryptography and Coding Theory

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Simplify an expression by applying quotient rule of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Learn the basics in simplifying an expression using the quotient rule of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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algebraic geometry 31 Rational maps

This lecture is part of an online algebraic geometry course, based on chapter I of "Algebraic geometry" by Hartshorne. It covers the definition of rational functions and rational maps, and gives an example of a cubic curve that is not birational to the affine line.

From playlist Algebraic geometry I: Varieties

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Andrew Wiles: Fermat's Last theorem: abelian and non-abelian approaches

The successful approach to solving Fermat's problem reflects a move in number theory from abelian to non-abelian arithmetic. This lecture was held by Abel Laurate Sir Andrew Wiles at The University of Oslo, May 25, 2016 and was part of the Abel Prize Lectures in connection with the Abel P

From playlist Sir Andrew J. Wiles

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Difference Quotient

What is a difference quotient? How to find a difference quotient. Deriving it from the rise over run formula.

From playlist Calculus

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Learn the basics for simplifying an expression using the rules of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Simplifying a monomial using the rules of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Andrew Wiles - The Abel Prize interview 2016

0:35 The history behind Wiles’ proof of Fermat’s last theorem 1:08 An historical account of Fermat’s last theorem by Dundas 2:40 Wiles takes us through the first attempts to solve the theorem 5:33 Kummer’s new number systems 8:30 Lamé, Kummer and Fermat’s theorem 9:10 Wiles tried to so

From playlist Sir Andrew J. Wiles

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John Voight, Belyi maps in number theory: a survey

VaNTAGe Seminar, August 17, 2021 License CC-BY-NC-SA

From playlist Belyi maps and Hurwitz spaces

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[ANT01] Algebraic number theory: an introduction, via Fermat's last theorem

The existence of the Euclidean algorithm is what makes multiplication in Z so nice. But some other rings have Euclidean algorithms too. Here's how we can exploit this for profit.

From playlist [ANT] An unorthodox introduction to algebraic number theory

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Schemes 40: Examples of PicX

This lecture is part of an online algebraic geometry course on schemes, based on chapter II of "Algebraic geometry" by Hartshorne. In this lecture we give some classic examples of Picard groups of schemes: class numbers of various number fields, complex curves, and some rational surfaces.

From playlist Algebraic geometry II: Schemes

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Learn how to simplify a monomial by applying quotient rule of exponents

👉 Learn how to simplify expressions using the quotient rule of exponents. The quotient rule of exponents states that the quotient of powers with a common base is equivalent to the power with the common base and an exponent which is the difference of the exponents of the term in the numerat

From playlist Simplify Using the Rules of Exponents | Quotient Rule

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Fukaya category for Landau-Ginzburg orbifolds and Berglund-HĂĽbsch homological...- Cheol-Hyun Cho

IAS/PU-Montreal-Paris-Tel-Aviv Symplectic Geometry Topic: Fukaya category for Landau-Ginzburg orbifolds and Berglund-HĂĽbsch homological mirror symmetry for curve singularities Speaker: Cheol-Hyun Cho Affiliation: Seoul National University Date: September 21, 2020 For more video please vi

From playlist Mathematics

Related pages

Wieferich prime | Full reptend prime | Pierre de Fermat | Primitive root modulo n | Wilson quotient | Logarithm | Fermat's little theorem | Mathematical proof | Cyclic number | Corollary | P-derivation | Wieferich pair | Integer | Gotthold Eisenstein | Number theory | Prime number | Parity (mathematics) | Modular arithmetic | Modular multiplicative inverse