Abstract
Let q be a prime power, and Fq be the finite field of order q. In this short note, by using methods from spectral graph theory, we give sufficient conditions to guarantee that Fq \ {0} {a1u1x1 + ... + adudxd : 1 ≤ xi ≤ Mi; 1 ≤ i ≤ d} ; where ai and ui are non-zero elements in Fq, and Mi are integers. This result generalizes a recent result given by Cilleruelo and Zumalacárregui (2014). Using the same techniques, we extend this result in the setting of the finite cyclic ring.
Sign-in/Register to access full text options 
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.
