Unsolved problems in number theory | Integer sequences | Mersenne primes | Perfect numbers | Divisor function
In number theory, a perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. For instance, 6 has divisors 1, 2 and 3 (excluding itself), and 1 + 2 + 3 = 6, so 6 is a perfect number. The sum of divisors of a number, excluding the number itself, is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum. Equivalently, a perfect number is a number that is half the sum of all of its positive divisors including itself; in symbols, where is the sum-of-divisors function. For instance, 28 is perfect as 1 + 2 + 4 + 7 + 14 = 28. This definition is ancient, appearing as early as Euclid's Elements (VII.22) where it is called τέλειος ἀριθμός (perfect, ideal, or complete number). Euclid also proved a formation rule (IX.36) whereby is an even perfect number whenever is a prime of the form for positive integer —what is now called a Mersenne prime. Two millennia later, Leonhard Euler proved that all even perfect numbers are of this form. This is known as the Euclid–Euler theorem. It is not known whether there are any odd perfect numbers, nor whether infinitely many perfect numbers exist. The first few perfect numbers are 6, 28, 496 and 8128 (sequence in the OEIS). (Wikipedia).
Perfect Numbers and Euler's Theorem
A perfect number is a number that equals the sum of its proper factors. How can we find them?
From playlist Math Play
MATH1081 Discrete Maths: Chapter 3 Question 29
Here we show there exists a perfect number. Presented by Peter Brown of the School of Mathematics and Statistics, Faculty of Science, UNSW.
From playlist MATH1081 Discrete Mathematics
HowStuffWorks Trivia! (General Knowledge No. 9)
What is a "perfect number"? Find out in this general knowledge video quiz. And yep, answers are included.
From playlist Quizz
Numbers in numerology and astrology that symbolise friendship and love.
From playlist My Maths Videos
One of the oldest unsolved math problems is studying odd perfect numbers. Have fun learning the many math approaches to this problem.
From playlist Summer of Math Exposition 2 videos
Exploring an amazing pattern that forms when we multiply numbers built only with the one digit
From playlist Number Patterns
How to take the square root of a number using prime factorization, sqrt(64)
👉 Learn how to find the square root of a number. To find the square root of a number, we identify whether that number which we want to find its square root is a perfect square. This is done by identifying a number which when raised to the 2nd power gives the number which we want to find it
From playlist How to Simplify the Square Root of a Number
Evaluate the square root of a perfect square number multiplied
👉 Learn how to find the square root of a number. To find the square root of a number, we identify whether that number which we want to find its square root is a perfect square. This is done by identifying a number which when raised to the 2nd power gives the number which we want to find it
From playlist Simplify the Square Root Expressions
The Six Triperfect Numbers - Numberphile
Check out Brilliant (and get 20% off their premium service): https://brilliant.org/numberphile (sponsor) More links & stuff in full description below ↓↓↓ This video features Dr James Grime - http://singingbanana.com Catch James in a recent Objectivity video with Brady: https://youtu.be/B
From playlist Perfect Numbers on Numberphile
Illustrative Mathematics Grade 6 - Unit 1- Lesson 17
Illustrative Mathematics Grade 6 - Unit 1- Lesson 17 Open Up Resources (OUR) If you have any questions, please contact me at dhabecker@gmail.com
From playlist Illustrative Mathematics Grade 6 Unit 1
Perfect Numbers and Mersenne Primes
Perfect numbers and Mersenne primes might seem like unrelated branches of math, but work by Euclid and Euler over 2000 years apart showed they are so deeply connected that a one-to-one correspondence exists between the even perfect numbers and the Mersenne primes. The existence of odd perf
From playlist Mathstars
MegaFavNumbers-The super rare sublime numbers
#MegaFavNumbers Relevant sources and links: https://www.mathpages.com/home/kmath202/kmath202.htm https://en.wikipedia.org/wiki/Euclid%E2%80%93Euler_theorem https://proofwiki.org/wiki/Sigma_Function_is_Multiplicative https://math.stackexchange.com/questions/3621899/proof-for-formula-for-num
From playlist MegaFavNumbers
Gabriele NEBE - Lattices, Perfects lattices, Voronoi reduction theory, modular forms, ...
Lattices, Perfects lattices, Voronoi reduction theory, modular forms, computations of isometries and automorphisms The talks of Coulangeon will introduce the notion of perfect, eutactic and extreme lattices and the Voronoi's algorithm to enumerate perfect lattices (both Eulcidean and He
From playlist École d'Été 2022 - Cohomology Geometry and Explicit Number Theory
Factoring Polynomials Completely - All Types (100 Problems & Free Worksheet)
Learn how to factor polynomials completely in this video math tutorial by Mario's Math Tutoring. We will be going through 100 factoring problems including greatest common factor, difference of 2 squares, sum and difference of 2 cubes, perfect square trinomials, trinomials with leading coe
From playlist Factoring - All Different Types
Why are Mersenne primes and perfect number related? | SoME contest entry
In this video, I explain how Mersenne primes are related to perfect numbers, go over the Euclid half of the Euclid-Euler theorem, and make a bunch of really terrible "jokes". This video is my submission to the 3Blue1Brown Summer of Math Exposition contest. Consider checking out some other
From playlist Summer of Math Exposition Youtube Videos
Intermediate Algebra Lecture 10.3 Part 2
Intermediate Algebra Lecture 10.3 Part 2: Simplifying Radical Expressions
From playlist Intermediate Algebra Playlist 1
Interesting Facts About the Last Digits of Prime Numbers
This video explains some interesting facts about the last digits of prime numbers.
From playlist Mathematics General Interest