Ben Green's Open Problem 63

Let $A$ be the smallest set containing $2$ and $3$ and such that $a_1a_2 - 1 \in A$ if $a_1, a_2 \in A$. Does $A$ have positive density?

Reference:

• [Ben Green's Open Problem 63](https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#section.8 Problem 63)
• erdosproblems.com/424