Numeric properties of 2025 | Raku for Prediction
This blog post demonstrates mathematical properties for the number 2025.| Raku for Prediction
The “Freshman’s dream” is the statement (x + y)p = xp + yp It’s not true in general, but it is true mod p if p is a prime. It’s a cute result, but it’s also useful in applications, such as finite field computations in cryptography. Here’s a demonstration of the Freshman’s dream in Python. >>> p = […] The post Freshman’s dream first appeared on John D. Cook.| John D. Cook
I recently saw someone post [1] that 987654321/123456789 is very nearly 8, specifically 8.0000000729. I wondered whether there’s anything distinct about base 10 in this. For example, would the ratio of 54321six and 12345six be close to an integer? The ratio is 4.00268, which is pretty close to 4. What about a larger base? Let’s […] The post 987654321 / 123456789 first appeared on John D. Cook.| John D. Cook
In 2013, John Conway and Alex Ryba published a brief note [1] on how to convert identities involving sine and cosine into identities involving Fibonacci and Lucas numbers. Fibonacci and Lucas The Fibonacci numbers Fn are defined by F0 = 0, F1 = 1, and Fn+2 = Fn + Fn+1 for n > 1. Similarly, […] The post Turning trig identities into Fibonacci identities first appeared on John D. Cook.| John D. Cook
This morning I took an old blog post and turned it into an X thread. I think the thread is easier to read. More expository and less rigorous. The post and thread look at generalizations of the fact that every integer and its fifth power end in the same digit. The conclusion is that n and nk […] The post More on Carmichael first appeared on John D. Cook.| John D. Cook
RSA public keys are usually the product of two primes, but they could be the product of multiple primes, and sometimes they are for digital signatures.| John D. Cook
My feed was recently clogged up with news articles reporting that Sam Altman thinks that AGI is here, or will be here next year, or whatever. I will refrain from giving even more air to this nonsense by linking to … Continue reading →| Xena
For any x, the behavior of multiples of x mod 1 is easy to classify. The powers of x mod 1 are more interesting. We give examples of different behavior.| John D. Cook
This blog post presents various visualizations related to the Collatz conjecture using Raku.| Raku for Prediction
Този блог пост представя различни визуализации, свързани с хипотезата на Колац, използвайки Raku.| Raku for Prediction
This blog post demonstrates mathematical properties for the number 2025.| Raku for Prediction
Update: Let me mention a ninth paper that just appeared on the arXive. IX. … and the optimal sofa for the moving sofa problem is … Gerver’s sofa. Optimality of Gerver’s Sofa…| Combinatorics and more
This week’s Fiddler is about tiling a square with smaller squares. Suppose you have infinitely many 3-by-3 cm tiles and infinitely many 5-by-5 cm tiles. You want to use some of these tiles to precisely cover a square whose side length is a whole number of centimeters. Tiles may not overlap, and they must completely … Continue reading "Tiling squares" The post Tiling squares first appeared on Book Proofs.| Book Proofs
Diffie-Hellman key agreement protocol uses modular exponentiation and calls for use of special prime numbers. If you ever wondered why, I’ll try to explain. Diffie-Hellman key agreement The &…| securitypitfalls
Having been through the process of finding and applying for postdoc positions in Europe over the last couple of years, here is now the big list that I wished someone had given me a few years ago.| Motivic stuff
In 2018 Harvard held a week-long celebration for Barry Mazur’s 80th birthday. In keeping with Mazur’s wide-ranging interests, and with the title — Mathematics Is a Long Conversation — t…| Mathematics without Apologies, by Michael Harris
