Year: 2026
Type: preprint
Abstract: A binomial coefficient $\binom{n}{k}$ is good if all its prime divisors exceed $k$, and its deficiency is the number of $k$-smooth integers in $(n-k,n]$. A short constructive proof of the existence of infinitely many good binomial coefficients with deficiency exactly one is given, which provides an answer to a problem of Erdős, Lacampagne, and Selfridge.
Source: arXiv (Cornell University)
Author: Zhang, Xu
Institution: Shandong University
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214107501