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

Open the contributing 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

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