pith. sign in

arxiv: 1809.01532 · v2 · pith:S4GSVNIWnew · submitted 2018-09-03 · 🧮 math.NT

On practical numbers of some special forms

classification 🧮 math.NT
keywords practicalinfinitelymanynumberssomethereformsintegers
0
0 comments X
read the original abstract

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

This paper has not been read by Pith yet.

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.