In arithmetic, an odd composite integer n is called an Euler pseudoprime to base a, if a and n are coprime, and (where mod refers to the modulo operation). The motivation for this definition is the fact that all prime numbers p satisfy the above equation which can be deduced from Fermat's little theorem. Fermat's theorem asserts that if p is prime, and coprime to a, then ap−1 ≡ 1 (mod p). Suppose that p>2 is prime, then p can be expressed as 2q + 1 where q is an integer. Thus, a(2q+1) − 1 ≡ 1 (mod p), which means that a2q − 1 ≡ 0 (mod p). This can be factored as (aq − 1)(aq + 1) ≡ 0 (mod p), which is equivalent to a(p−1)/2 ≡ ±1 (mod p). The equation can be tested rather quickly, which can be used for probabilistic primality testing. These tests are twice as strong as tests based on Fermat's little theorem. Every Euler pseudoprime is also a Fermat pseudoprime. It is not possible to produce a definite test of primality based on whether a number is an Euler pseudoprime because there exist absolute Euler pseudoprimes, numbers which are Euler pseudoprimes to every base relatively prime to themselves. The absolute Euler pseudoprimes are a subset of the absolute Fermat pseudoprimes, or Carmichael numbers, and the smallest absolute Euler pseudoprime is 1729 = 7×13×19. (Wikipedia).
This video given Euler's identity, reviews how to derive Euler's formula using known power series, and then verifies Euler's identity with Euler's formula http://mathispower4u.com
From playlist Mathematics General Interest
Euler Pronunciation: In Depth Analysis
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From playlist Fun and Amazing Math
Euler’s method - How to use it?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Euler’s method is a numerical method that you can use to approximate the solution to an initial value problem with a differential equation that can’t be solved using a more traditional method,
From playlist Differential Equations
Fermat’s HUGE little theorem, pseudoprimes and Futurama
A LOT of people have heard about Andrew Wiles solving Fermat's last theorem after people trying in vain for over 350 years. Today's video is about Fermat's LITTLE theorem which is at least as pretty as its much more famous bigger brother, which has a super pretty accessible proof and which
From playlist Recent videos
Linear Algebra 21g: Euler Angles and a Short Tribute to Leonhard Euler
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 3 Linear Algebra: Linear Transformations
"Fortunately, Unfortunately": How to Tell Whether a Number Is Prime #MegaFavNumbers
How can we tell whether or not a large integer is prime? Well, there's some bad news and some good news (and more bad news, and more good news, and...) My contribution to #MegaFavNumbers (and my first go at YouTube, so, you know, go easy on me). Matt Parker's video, which got me thinking
From playlist MegaFavNumbers
C39 A Cauchy Euler equation that is nonhomogeneous
A look at what to do with a Cauchy Euler equation that is non-homogeneous.
From playlist Differential Equations
How Shor's Algorithm Factors 314191
Go to http://www.dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium! Watch the main video: https://www.youtube.com/watch?v=lvTqbM5Dq4Q Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics This video ex
From playlist MinutePhysics
How they found the World's Biggest Prime Number - Numberphile
Featuring Matt Parker... More links & stuff in full description below ↓↓↓ See part one at: https://youtu.be/tlpYjrbujG0 Part three on Numberphile2: https://youtu.be/jNXAMBvYe-Y Matt's interview with Curtis Cooper: https://youtu.be/q5ozBnrd5Zc The previous record: https://youtu.be/QSEKzFG
From playlist Matt Parker (standupmaths) on Numberphile
How Quantum Computers Break Encryption | Shor's Algorithm Explained
Go to http://www.dashlane.com/minutephysics to download Dashlane for free, and use offer code minutephysics for 10% off Dashlane Premium! Support MinutePhysics on Patreon! http://www.patreon.com/minutephysics This video explains Shor’s Algorithm, a way to efficiently factor large pseudop
From playlist MinutePhysics
B11 The improved Euler Formula
The improved Euler Formula using Python.
From playlist A Second Course in Differential Equations
Advice for amateur mathematicians | More magic, with Euler numbers and Euler polynomials | Wild Egg
From the Bernoulli numbers and Bernoulli polynomials, it is a small step to consider Euler numbers and Euler polynomials. We of course pursue our basic strategy of incorporating these things into our two dimensional number theoretic point of view, and then utilizing linear algebra / matrix
From playlist Maxel inverses and orthogonal polynomials (non-Members)
I continue the look at higher-order, linear, ordinary differential equations. This time, though, they have variable coefficients and of a very special kind.
From playlist Differential Equations
Differential Equations | Euler Equations Example 2
We solve a second order differential equation known as an Euler equation. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Differential Equations
Mandelbrot fractal zoom // featuring Euler bio
Mandelbrot fractal zoom // featuring Euler bio Come hang out and watch a fractal zoom through the Mandelbrot set. To celebrate Euler's contributions to mathematics, this video features a brief bio. of Leonhard Euler! ---------------------------------------------------------------------
From playlist Misc.
Math Explorations Ep22, Euler circuits & paths (Mar 23, 2022)
This is a recording of a live class for Math 1015, Mathematics: An Exploration, an undergraduate course for non-technical majors at Fairfield University, Spring 2022. The major topics are voting, gerrymandering, and graph theory. Handouts and homework are at the class website. Class web
From playlist Math 1015 (Mathematical Explorations) Spring 2022
Graph Theory: Euler Paths and Euler Circuits
This lesson explains Euler paths and Euler circuits. Several examples are provided. Site: http://mathispower4u.com
From playlist Graph Theory
MA 15: Euler circuits and paths
This video is for my Spring 2020 section of MA 15, for the class meeting on Friday April 3. Fast forward music is from "Now Get Busy" by the Beastie Boys, licensed Creative Commons Noncommercial Sampling Plus.
From playlist Math 15 Spring 2020
Euler's Differential Equation Introduction
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From playlist Differential Equations