# Knots and ones

## TL;DR

This paper provides a number theoretic proof of the integrality and divisibility properties of certain knot invariants called BPS invariants, using formulas involving binomial coefficients and the Möbius function.

## Contribution

It introduces a new number theoretic proof for the integrality and divisibility of BPS invariants of knots, advancing understanding of their algebraic properties.

## Key findings

- Proved the integrality of specific BPS invariants of knots.
- Established divisibility properties conjectured for these invariants.
- Derived formulas involving binomial coefficients and the Möbius function.

## Abstract

We give a number theoretic proof of the integrality of certain BPS invariants of knots. The formulas for these numbers are sums involving binomial coefficients and the M\"obius function. We also prove a conjecture about further divisibility properties of the invariants.