Unsolved problems in number theory | Articles containing proofs | Constructible polygons | Integer sequences | Large integers | Classes of prime numbers
In mathematics, a Fermat number, named after Pierre de Fermat, who first studied them, is a positive integer of the form where n is a non-negative integer. The first few Fermat numbers are: 3, 5, 17, 257, 65537, 4294967297, 18446744073709551617, ... (sequence in the OEIS). If 2k + 1 is prime and k > 0, then k must be a power of 2, so 2k + 1 is a Fermat number; such primes are called Fermat primes. As of 2022, the only known Fermat primes are F0 = 3, F1 = 5, F2 = 17, F3 = 257, and F4 = 65537 (sequence in the OEIS); heuristics suggest that there are no more. (Wikipedia).
MATH3411 Information, Codes and Ciphers We use Fermat factorisation to factor one of the three integers given in the problem. Presented by Thomas Britz, School of Mathematics and Statistics, Faculty of Science, UNSW Australia
From playlist MATH3411 Information, Codes and Ciphers
6,700,417 - The prime which Proved Fermat Wrong. #MegaFavNumbers
Pierre de Fermat - of "Fermat's Last Theorem" fame - thought that 4,294,967,297, and all numbers of the form 2^(2^n)+1, were prime. But he was wrong! More about Fermat numbers (and primes) - https://en.wikipedia.org/wiki/Fermat_number This video is part of the #MegaFavNumbers project. If
From playlist MegaFavNumbers
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
How to prove Fermat's Last Theorem in under 7 seconds
How to prove Fermat's Last Theorem in under 7 seconds
From playlist My Maths Videos
Very Large Primes and (Almost) Perfect Numbers -- MegaFavNumbers
This is my video submission for the #MegaFavNumbers celebration. As promised in the video, here is the very large number that was simply too big for the screen: 5282945208034002678497845769960721106385426547566030332928651387255812371024044147692699871010305634389030253300042369944654409
From playlist MegaFavNumbers
Proof based on a comment of an earlier video - an example of Fermat Little Theorem
#mathonshorts #shorts Credit goes to "black third" https://www.youtube.com/channel/UCWt0aCW6TeP8PP5pdREfoag See comments from this video: https://youtu.be/NKpzfyCZAPg The Pigeonhole Principle was used in the other video. Here, we use Fermat Little Theorem to prove that the number of
From playlist Elementary Number Theory
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
A Short Course in Algebra and Number Theory - Fermat's little theorem and primes
To supplement a course taught at The University of Queensland's School of Mathematics and Physics I present a very brief summary of algebra and number theory for those students who need to quickly refresh that material or fill in some gaps in their understanding. This is the fifth lectur
From playlist A Short Course in Algebra and Number Theory
Primality (1 of 2: Fermat's Test)
From playlist Cryptography
Fermat's Last Theorem - Numberphile
Simon Singh on Fermat's Last Theorem. Simpsons book: http://amzn.to/1fKe4Yo Fermat book: http://amzn.to/1jWqMTa More links & stuff in full description below ↓↓↓ EXTRA FOOTAGE: http://youtu.be/FXbsIbRVios FERMAT IN SIMPSONS: http://youtu.be/ReOQ300AcSU Interview with Ken Ribet, who played
From playlist Numberphile Videos
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
Euler's and Fermat's last theorems, the Simpsons and CDC6600
NEW (Christmas 2019). Two ways to support Mathologer Mathologer Patreon: https://www.patreon.com/mathologer Mathologer PayPal: paypal.me/mathologer (see the Patreon page for details) This video is about Fermat's last theorem and Euler's conjecture, a vast but not very well-known genera
From playlist Recent videos
Why was this visual proof missed for 400 years? (Fermat's two square theorem)
Today's video is about a new really wonderfully simple and visual proof of Fermat's famous two square theorem: An odd prime can be written as the sum of two integer squares iff it is of the form 4k+1. This proof is a visual incarnation of Zagier's (in)famous one-sentence proof. 0:00 Intr
From playlist Recent videos
The Bridges to Fermat's Last Theorem - Numberphile
Ken Ribet - a key player in the solution to Fermat's Last Theorem - gives a taste of how real mathematics is done... piece by piece and by human beings. More links & stuff in full description below ↓↓↓ More Fermat (with Simon Singh): http://youtu.be/qiNcEguuFSA Even more Fermat (with Simo
From playlist Fermat's Last Theorem on Numberphile
Number Theory: Fermat's Little Theorem
An introduction to Fermat's Little Theorem and its applications
From playlist Basics: Number Theory
The Abel Prize announcement 2016 - Andrew Wiles
0:44 The Abel Prize announced by Ole M. Sejersted, President of The Norwegian Academy of Science and Letters 2:07 Citation by Hans Munthe-Kaas, Chair of the Abel committee 8:01 Popular presentation of the prize winners work by Alex Bellos, British writer, and science communicator 21:43 Pho
From playlist The Abel Prize announcements
Use Fermat Numbers to Prove the Infinitude of Prime Numbers
Use Fermat Numbers to Prove the Infinitude of Prime Numbers Please Like, Share, and Subscribe! https://www.youtube.com/channel/UC5uV1LcSkHL5zCxKBikdTEg?sub_confirmation=1
From playlist Elementary Number Theory