Erdős Problem 870

### What is the conjecture

https://www.erdosproblems.com/870

Let $k\geq 3$ and $A$ be an additive basis of order $k$. Does there exist a constant $c=c(k)>0$ such that if $r(n)\geq c\log n$ for all large $n$ then $A$ must contain a minimal basis of order $k$? (Here $r(n)$ counts the number of representations of $n$ as the sum of at most $k$ elements from $A$.)

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

### What is the conjecture