Some, however, find that bridging fields opens new realms of possibility. Henry Kvinge, who trained as a mathematician but ...

This requires an algorithm: students are taught to stack one number atop another and multiply each digit of the bottom number ...

You will learn how to add and subtract integers. We will work through adding and subtracting two integers up to multiple integers. We can look at adding and subtracting integers by looking at their ...

Digitally delicate prime numbers become composite with this one weird trick. Math researchers proved these primes exist using the bucket proof method. There are no known examples so far, but ...

The world of mathematics is full of unreachable corners, where unsolvable problems live. Now, yet another has been exposed. In 1900, the eminent mathematician David Hilbert announced a list of 23 key ...

Abstract: This paper presents efficient algorithms, designed to leverage SIMD for performing additions and Montgomery reductions on integers larger than 512 bits. The existing algorithms encounter ...

What is the largest natural number possible? By using the word natural, I have ruled out the possibility that you simply answer infinity (∞) to torpedo the guessing game. But even if we allowed ...

Msieve is the result of my efforts to understand and optimize how integers are factored using the most powerful modern algorithms. This documentation corresponds to version 1.54 of the Msieve library.

Abstract: Modular inversion, the multiplicative inverse of an integer in the ring of integers modulo a prime number, is widely used in public-key cryptography. However, it is one of the most ...

The algebraic K K-groups of the integers, and other rings, are a big deal. A lot of fairly recent progress on understanding them is due to Voevodsky, Rost, Rognes and Weibel, whose work culminated in ...