SU Math faculty presents research at International Mathematics Conference in Boracay

Assistant Professor Karlstein F. Diao of the Silliman University College of Arts and Sciences Mathematics Department presented his research paper titled “Integral Solutions of the Quadratic Diophantine Equation: x² + bx + c = y²” during the International Conference in Mathematics, Statistics, and Mathematics Education (ICMSME) and the 19th Annual Convention of the Mathematical Society of the Philippines (MSP) – Regions 10, 12, and BARMM.

The conference was held on October 27–29, 2025, at the Paradise Garden Resort Hotel and Convention Center in Boracay Island, Philippines.

In his presentation, Diao examined integer solutions of a class of quadratic Diophantine equations. His study established a refined principal theorem, supported by rigorous proofs, characterizing the conditions for the existence and solvability of solutions under both degenerate and non-degenerate cases.

The research detailed parity, inequality, and congruence constraints that govern the solutions, showing that the resulting solution sets may be either even or infinite in cardinality.

Diao’s study also introduced an automated algorithm designed to efficiently generate these integral solutions, translating theoretical results into a practical computational method, with potential extensions to more generalized forms of the equation.

The annual convention, organized in collaboration with MSP-Region 6, was co-hosted by Mindanao State University-Iligan Institute of Technology and West Visayas State University.

It featured plenary lectures, parallel sessions, and poster presentations that provided a venue for scholars to exchange ideas and present current research across mathematics, statistics, and mathematics education.

Parallel sessions covered a wide range of topics, including graph theory, mathematical modeling, statistics, number theory, algebra, and mathematics education.