Abstract
It is shown that the polynomials satisfying the identityf(x) f(x + 1) = f(x 2 +x − a), wherea either belongs to a field of characteristic zero or is transcendental over a prime field of characteristic exceeding 2, are precisely those of the form(x 2 −a) n ; thus extending a result proved by Nathanson in the complex case. The result is not, in general, true in characteristic 2. Additionally, a class of finite sets, considered by Nathanson in connection with the identity, is completely determined.
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.
