google-deepmind / google-deepmind/formal-conjectures
Erdős Problem 365
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ams-11: Number theory
erdos-problems
new conjecture
- Dominant language
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Description
### What is the conjecture
https://www.erdosproblems.com/365
Do all pairs of consecutive powerful numbers $n$ and $n+1$ come from solutions to the Pell equations? In other words, must either $n$ or $n+1$ be a square?Is the number of such $n\leq x$ bounded by $(\log x)^{O(1)}$?
Status: open
see also #372 #373 and #375
### 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
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