Random Finite Sum Sets and Product Sets in Subsets of the Natural Numbers
Sukrit Chakraborty, Sourav Kanti Patra · Global Integrated Mathematics · 2026
We investigate the occurrence of additive and multiplicative structures in random subsets of the natural numbers. Specifically, for a Bernoulli random subset of N where each integer is included independently with probability p ∈ (0, 1), we prove that almost surely such a set contains finite sumsets (FS-sets) and finite product sets (FP-sets) of every finite length. Then we prove any Bernoulli random subset of N contains a pattern of the form {x, y, x + y, xy}, giving a random solution of the Hindman conjecture.