A Note on a Result of Makowski
Luis H. Gallardo, Joshua Zelinsky
TL;DR
This paper addresses a correction in a previous proof regarding the unique even perfect number that is the sum of two perfect cubes, and explores related cases for higher powers.
Contribution
It corrects a gap in a prior proof and extends discussion to the case of higher powers in the context of perfect numbers.
Findings
28 is the only even perfect number that is the sum of two perfect cubes
The paper clarifies the proof and discusses higher power cases
Provides insights into the structure of perfect numbers and their representations
Abstract
In this note, we fix a gap in a proof of the first author that 28 is the only even perfect number which is the sum of two perfect cubes. We also discuss the situation for higher powers.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAnalytic Number Theory Research · Mathematics and Applications · Meromorphic and Entire Functions