What is a Quadratic Residue? - Definition and Example
Quadratic residues are an important part of elementary number theory. Here we explain the definition of a quadratic residue mod p, go through an example of finding quadratic residues, and note one basic property. Quadratic Residues playlist: https://www.youtube.com/playlist?list=PLug5ZIRr
From playlist Quadratic Residues
Theory of numbers: Quadratic residues
This lecture is part of an online undergraduate course on the theory of numbers. We define quadratic residues (squares) and describe their basic properties, in particular Euler's criterion. The we describe fast algorithms to test whether a number is a quadratic residue, and if so to find
From playlist Theory of numbers
Number Theory | Quadratic Residues: Definition and Examples
From King's Landing, we give the definition of a quadratic residue modulo n as well as a few examples. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Number Theory
Number Theory | A quadratic formula mod p??
From Kings Landing, we discover the solvability of an arbitrary quadratic congruence modulo an odd prime p. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Quadratic Residues, the Legendre Symbol, and Quadratic Reciprocity
Quadratic Residues Always Have Even Index
Congruence of powers of primitive roots: https://youtu.be/TfZ9nPfOhQ0 Intro to Indices: https://youtu.be/jLeNX2jYuUs Intro to Quadratic Residues: https://youtu.be/M6gDsFhQugM When working with quadratic residues, it's useful to leverage our knowledge of indices. Here we prove a few key
From playlist Quadratic Residues
Solving using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula With Missing Terms
Find the complex roots of an equation using the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | Equation
How to apply the quadratic formula to find one solution
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Introduction to number theory lecture 31. Quadratic residues.
This lecture is part of my Berkeley math 115 course "Introduction to number theory" For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj53L8sMbzIhhXSAOpuZ1Fov8 We cover some basic properties of quadratic residues, and use Gauss's lemma to find the pri
From playlist Introduction to number theory (Berkeley Math 115)
The discriminant and finding the solutions using quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | x^2+bx+c
Quadratic Residues — Number Theory 22
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From playlist Number Theory
Quadratic Residues -- Number Theory 22
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From playlist Number Theory v2
Particle collisions, hypergroups and quadratic residues | Diffusion Symmetry 3 | N J Wildberger
We introduce a simple particle collision model for the algebraic structure called a hypergroup, which is a normalization of a fusion rule algebra, and closely connected also to Bose Messner algebras and association schemes from algebraic combinatorics. In this model, the results of parti
From playlist Diffusion Symmetry: A bridge between mathematics and physics
Euler's Criterion: Proof and Example
Proof that quadratic residues always have even index: https://youtu.be/zs0ZtQzVBSE Intro to indices: https://youtu.be/jLeNX2jYuUs Euler's criterion is one way to determine whether a number is a quadratic residue mod p. Here we prove Euler's criterion and give an explanation for why it
From playlist Quadratic Residues
Lehmer Factor Stencils: A paper factoring machine before computers
In 1929, Derrick N. Lehmer published a set of paper stencils used to factor large numbers by hand before the advent of computers. We explain the math behind the stencils, which includes modular arithmetic, quadratic residues, and continued fractions, including my favourite mathematical vi
From playlist Joy of Mathematics
Number Theory | The Legendre Symbol and Euler's Criterion
We present a definition of the Legendre symbol and Euler's criterion to calculate it quickly. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Mathematics named after Leonhard Euler
Learn to find the solutions of a quadratic by applying the quadratic formula
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c