PROVED
This has been solved in the affirmative.
Let $\alpha>0$ be a real number, not an integer. The density of integers $n\geq 1$ for which $(n,\lfloor n^\alpha\rfloor)=1$ is $6/\pi^2$.
|
Likes this problem
|
None
|
|
Interested in collaborating
|
None
|
|
Currently working on this problem
|
None
|
|
This problem looks difficult
|
None
|
|
This problem looks tractable
|
None
|
|
The results on this problem could be formalisable
|
None
|
|
I am working on formalising the results on this problem
|
None
|
When referring to this problem, please use the original sources of Erdős. If you wish to acknowledge this website, the recommended citation format is:
T. F. Bloom, Erdős Problem #1149, https://www.erdosproblems.com/1149, accessed 2026-04-11
