Abstract
A perfect polynomial A\in\mathbb{F}_4[x] is a monic polynomial that equals the sum of its monic divisors. There are no perfect polynomials A\in\mathbb{F}_4[x] with exactly 3 prime divisors, i.e., of the form A=P^aQ^bR^c where P,Q,R\in\mathbb{F}_4[x] are irreducible and a,b,c are positive integers. We characterize the perfect polynomials A with 4 prime divisors such that one of them has degree 1 . Assume that A has an arbitrary number of distinct prime divisors, we discuss some simple congruence obstructions that arise and we propose three conjectures.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
