2018/09/03 by Wang, Li-Yuan, Sun, Zhi-Wei
#11B83 #11D09 #FOS: Mathematics #Number Theory (math.NT)
paper · doi:10.48550/arxiv.1809.01532
In this paper we study practical numbers of some special forms. For any integers b≥0 and c>0, we show that if n2+bn+c is practical for some integer n>1, then there are infinitely many nonnegative integers n with n2+bn+c practical. We also prove that there are infinitely many practical numbers of the form q4+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).