Papers › On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}

On the Elementary Symmetric Functions of {1,1/2,…,1/n}\{1/i}

25 Feb 2025arXiv:2502.18267links table onlyarchive 2025-07-28

Weilin Zhang, Hongjian Li, Sunben Chiu, Pingzhi Yuan

The archive published only this paper's code-link row. Authors, date and abstract are from arXiv's metadata (CC0), read from the Kaggle arXiv metadata snapshot of 2026-09-12 where its title matched the archive's; the title is the archive's.

In 1946, P. Erd\H{o}s and I. Niven proved that there are only finitely many positive integers n for which one or more of the elementary symmetric functions of 1,1 / 2, ⋯, 1 / n are integers. In 2012, Y. Chen and M. Tang proved that if n ⩾4, then none of the elementary symmetric functions of 1,1 / 2, ⋯, 1 / n are integers. In this paper, we prove that if n ⩾5, then none of the elementary symmetric functions of {1,1 / 2, ⋯, 1 / n} \{1 / i} are integers except for n=i=2 and n=i=4.

PaperPDFCode

Code

zsben2/esf official report

Repository list and official/mentioned flags are the archive's, frozen 2025-07-28. Reachability, where shown, is from one Syntology probe window (2026-09-16 to 2026-09-18); repositories not probed show nothing. GitHub stars are not tracked.

Code Syntology ran Syntology

Not run by Syntology. Nothing on this page verifies that the listed code works.

Results from the paper archive 2025-07-28

No leaderboard rows for this paper in the archive.

Report a problem or propose a change · a person checks every report against the paper or source before anything changes; decisions are listed on /corrections