On the Solvability of Systems of Equations Revisited

Authors

• Steven Senger, Missouri State UniversityFollow
• Thang Pham, Vietnam National University, Hanoi
• Nguyen Trung-Tuan, Hanoi-Amsterdam High School for the Gifted
• Nguyen Duc-Thang, University of Science, Viet Nam National University Ho Chi Minh City
• Le Anh Vinh, Vietnam National Institute of Educational Sciences

Abstract

In this paper, we introduce a new and direct approach to study the solvability of systems of equations generated by bilinear forms. More precisely, let B(·,·) be a non-degenerate bilinear form and E be a set in Fq2. We prove that if |E|?q5/3 then the number of triples (B(x, y), B(y, z), B(z, x)) with x,y,z?E is at least cq3 for some positive constant c. This significantly improves a result due to the fifth listed author (2009).

Department(s)

Mathematics

Document Type

Article

DOI

10.1007/s10013-025-00771-w

Keywords

Finite fields, Simplex, Solvability of systems, Triangles

Publication Date

1-1-2025

Recommended Citation

Senger, Steven; Pham, Thang; Trung-Tuan, Nguyen; Duc-Thang, Nguyen; and Vinh, Le Anh, "On the Solvability of Systems of Equations Revisited" (2025). Faculty Scholarship. 291.
https://bearworks.missouristate.edu/articles00/291

Journal Title

Vietnam Journal of Mathematics