# Fractal Sets and Arithmetic Progressions

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.

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.

Which integers are a multiple of the sum of their “small” divisors? In the post, we study whether this set should be finite or not.

Our partial solution relates this problem to many outstanding conjectures in number theory about the distribution of prime numbers, such as the twin prime conjecture and the infinitude of Mersenne primes.