English

On practical numbers of some special forms

Number Theory 2019-07-12 v2

Abstract

In this paper we study practical numbers of some special forms. For any integers b0b\ge0 and c>0c>0, we show that if n2+bn+cn^2+bn+c is practical for some integer n>1n>1, then there are infinitely many nonnegative integers nn with n2+bn+cn^2+bn+c practical. We also prove that there are infinitely many practical numbers of the form q4+2q^4+2 with qq practical, and that there are infinitely many practical Pythagorean triples (a,b,c)(a,b,c) with gcd(a,b,c)=6\gcd(a,b,c)=6 (or gcd(a,b,c)=4\gcd(a,b,c)=4).

Keywords

Cite

@article{arxiv.1809.01532,
  title  = {On practical numbers of some special forms},
  author = {Li-Yuan Wang and Zhi-Wei Sun},
  journal= {arXiv preprint arXiv:1809.01532},
  year   = {2019}
}

Comments

6 pages, refined version

R2 v1 2026-06-23T03:55:11.471Z