Research Groups Number Theory
Number Theory Research Group focuses on determining the existence or non-existence of solutions of various types of exponential Diophantine equations. If solutions exist, the group tries to use elementary methods and other techniques to check whether there are finitely many or infinitely many solutions, and eventually find all solutions. The group also considers problems that are related to different types of prime numbers and their applications. The group is also exploring topics that involve elliptic curves and the circle method.
Joy Ascaño Students
Jerwin De Leon
Steven Karl Gantala
Jesielyn Mae Ado
Julius Fergy Rabago
John Raphael Antalan
Ron Allan Baran
Anna Clarice Yanday
Renz Jimwel Mina
• Mina, Renz Jimwel S. (2023). Ranks of Elliptic Curves and the θ-Congruent Number Problem, Dissertation.
• Taclay, Richard J. (2023). On Some Fermat Quartic nx
4 + y 4 = z 4, Master's Thesis. • Yanday, Anna Clarice M. (2023). On the Diophantine Equations p
qx± (p q + 1) y =z 2 and (p q + 1) x - p qy=z 2, Master's Thesis. • Bigcas, Rocky A. and De la Cruz, Nathaniel Chane C.(2023). Exploration on the Non-negative Solutions of the Diophantine Equations of the form a
x + b y + c z = w 2, Bachelor's Thesis. • Avenilla, Merlyn C. (2022). On the Solutions of the Equation p
x + (p+5k) y = z 2, Bachelor's Thesis. • Calabia, Ednalyn Xyra P. (2022). On the Solutions of the Diophantine Equation u
a + v b = z 2 for prime pairs u and v, Bachelor's Thesis. • Julongbayan, Zyrene Mae U. (2022). Explorations on the Diophantine Equation a
x + b y + c z = w 2, Bachelor's Thesis. • Caasi, Kenneth S. (2022). On a Modified Giuga's Congruence, Master's Thesis.
• Baran, Ron Allan V. (2020). Estimating the number of pairs of primes of the form p and 4p+3 using the circle method, Master's Thesis.
• Gayo, William Jr. S. (2020). On Some Mersenne Prime-Involved Exponential Diophantine Equations of the form a
x ± b y = z 2n, Master's Thesis. • Mina, Renz Jimwel S. (2020). On Exponential Diophantine Equations of the form p
x +q y = z n, Master's Thesis. • Aquino, Ronald L. (2019). On Solving Diophantine Equations of the form p
x +q y = z 3, Master's Thesis. • Antalan, John Rafael M. (2017). On Solving The Even Almost Perfect Number Problem: Some Approaches and Some New Results, Master's Thesis.
• Rabago, Julius Fergy T. (2017). Shape Optimization for the Bernoulli Free Boundary Problem Via Céa’s Classical Lagrange Method and Min-Max Differentiability of the Lagrangian, Master's Thesis.