Erdős Problem 436

### What is the conjecture

https://www.erdosproblems.com/436

If $p$ is a prime and $k,m\geq 2$ then let $r(k,m,p)$ be the minimal $r$ such that $r,r+1,\ldots,r+m-1$ are all $k$-th power residues modulo $p$. Let
$$\Lambda(k,m)=\limsup_{p\to \infty} r(k,m,p).$$
Is it true that $\Lambda(k,2)$ is finite for all $k$? Is $\Lambda(k,3)$ finite for all odd $k$? How large are they?

Status: open

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

Start by reading the conjecture at erdosproblems.com/436 and reviewing the formal-conjectures repository to find how similar Erdős problems are represented. Done means adding a formal Lean statement for the conjecture, but this issue names no files, tests, or implementation entry point.

Written by the indexing model from the issue text.