Polynomials with divisors of every degree

JOURNAL OF NUMBER THEORY

卷:132

Article

Thompson, Lola

关键词: Polynomials;    Practical numbers;    Euler totient function;   

DOI  :  10.1016/j.jnt.2011.10.005

来源: Elsevier

【 摘 要 】

We consider polynomials of the form t(n) - 1 and determine when members of this family have a divisor of every degree in Z[t]. With F(x) defined to be the number of such integers n <= x, we prove the existence of two positive constants c(1) and c(2) such that c(1) x/log x <= F(x) <= c(2) x/log x. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free