Green's Open Problems #61

### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.61

Suppose that $A + A$ contains the first $n$ squares. Is $|A| \geq n^{1-o(1)}$?

### [AMS categories](https://github.com/google-deepmind/formal-conjectures/labels?q=ams-)

* ams-11

### Choose either option
- [ ] I plan on adding this conjecture to the repository
- [x] This issue is up for grabs: I would like to see this conjecture added by somebody else

Start with Green's Open Problems PDF, specifically problem 61, to understand the conjecture about sets whose sumset contains the first n squares. Then inspect the repository's existing formalized conjectures for the expected form; done means the conjecture has been added to the repository.

Written by the indexing model from the issue text.