Category Archives: Number Theory
$p$-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
A Generalized Fun Integral Problem (and Particular Values of the Riemann $\zeta$ Function)
In an earlier post, titled A Fun Integral Problem, I gave a calculation for an integral as an infinite sum $\sum_{n=1}^{\infty}\frac{1}{n^{2}}$. I’ve been told that I should generalize it, so I’ll do that here (hence the title). I will also … Continue reading