google-deepmind / google-deepmind/formal-conjectures
Green's Open Problems #98
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Description
### What is the conjecture
https://people.maths.ox.ac.uk/greenbj/papers/open-problems.pdf#problem.98
Let $d \geq 3$ be an odd integer. Give bounds on $\nu(d)$ such that if $n > \nu(d)$ the following is true: given any homogeneous polynomial $F(\mathbf{x}) = F(x\_1, ..., x\_n) \in \mathbb{Z}[x\_1, ..., x\_n]$ of degree $d$, there is some $\mathbf{x} \in \mathbb{Z}^n \setminus \\{\mathbf{0}\\}$ such that $F(\mathbf{x}) = 0$.
### [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
Contributor guide
Research direction
Start by reading the linked Green's Open Problems PDF, specifically problem 98, and inspect existing formalized conjectures in the repository for the expected structure. Done means adding a formal statement of the conjecture to the repository and ensuring it passes the project's checks.
Written by the indexing model from the issue text.
Assessment
- Domain
- tooling
- Issue type
- Feature
- Difficulty
- 5/5
- Estimated time
- Over a week
- Activity status
- Stale
- Clarity
- Needs clarification
- Newbie friendliness
- 30/100