Category Archives: Programming
$p$-adic Valuation and the bsf / tzcnt and popcnt Instructions
Today, we’ll be looking at $p$-adic valuation defined on the integers, with a specific look at a special formula for finding the $p$-adic valuation of $n!$ for any given $n.$ We won’t be as concerned about optimizations this time, since … Continue reading
bsf / tzcnt and popcnt Instructions
Erdős–Straus Conjecture and Computing
While looking through some of my older programming projects, I found my old Egyptian Form project, which implements a greedy algorithm described by Solomon W. Golomb [1] for turning any fraction of positive integers into a sum of reciprocals of … Continue reading
On The Product of All Primes Between $N$ and $2N$ Compared to $2^{N}$
While reading some course notes from MIT 18.703 (Modern Algebra), I came across the following statement on page 3: Lemma 22.3. The product of all primes $r$ between $N$ and $2N$ is greater than $2^{N}$. However, this can quickly be … Continue reading