Stirling’s approximation gives a useful estimate for large factorials. This post contains a (new?) proof of Stirling’s formula which relies on properties of the Riemann zeta function.
If a set of positive integers contains no arithmetic progressions, how large can it be? In this post, we study this question in the context of harmonic sums.
This post discusses the problem of computer-assisted decryption of un-parsed substitution ciphers. Sample Mathematica code is linked within.
Most factorization algorithms in use today fit in one of two camps: sieve-based methods based on congruences of squares, and algorithms based on decompositions of algebraic groups. In this article, we trace the common thread connecting the latter.
In this post, I discuss the method of prosthaphaeresis, a proto-logarithm that enabled celestial navigation for the quarter-century predating the introduction of Napier’s logarithm.
The integral formula for secant is often introduced in a very artificial way. In this post, I look at the history of this integral and give several derivations.
One of Landau’s four problems from 1912 concerns the infinitude of primes in the values of a certain quadratic polynomial.
In this post, we show that the largest prime factors of the values of this polynomial are “relatively large” infinitely often.