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Number Theory

The 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.

Faculty
  1. Jerico Bacani
  2. Renz Mina
  3. Joy Ascaño

Students
  1. Jerwin De Leon
  2. Jasper Constantino
  3. Steven Karl Gantala
  4. Ranie Azote
  5. Mylene Reyes
  6. Jesielyn Mae Ado

Graduates
  1. Julius Fergy Rabago
  2. John Raphael Antalan
  3. Ronald Aquino
  4. Ron Allan Baran
  5. Kenneth Caasi
  6. Anna Clarice Yanday
  7. Richard Taclay
  8. Renz Jimwel Mina

  1. Regular Meetings
  2. Workshops
  3. Research Dissemination

  1. • Mina, Renz Jimwel S. (2023). Ranks of Elliptic Curves and the θ-Congruent Number Problem, Dissertation.
  2. • Taclay, Richard J. (2023). On Some Fermat Quartic nx4 + y4 = z4, Master's Thesis.
  3. • Yanday, Anna Clarice M. (2023). On the Diophantine Equations pqx± (pq + 1)y =z2 and (pq + 1)x - pqy=z2, Master's Thesis.
  4. • Bigcas, Rocky A. and De la Cruz, Nathaniel Chane C.(2023). Exploration on the Non-negative Solutions of the Diophantine Equations of the form ax + by + cz = w2, Bachelor's Thesis.
  5. • Avenilla, Merlyn C. (2022). On the Solutions of the Equation px + (p+5k)y = z2, Bachelor's Thesis.
  6. • Calabia, Ednalyn Xyra P. (2022). On the Solutions of the Diophantine Equation ua + vb = z2 for prime pairs u and v, Bachelor's Thesis.
  7. • Julongbayan, Zyrene Mae U. (2022). Explorations on the Diophantine Equation ax + by + cz = w2, Bachelor's Thesis.
  8. • Caasi, Kenneth S. (2022). On a Modified Giuga's Congruence, Master's Thesis.
  9. • 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.
  10. • Gayo, William Jr. S. (2020). On Some Mersenne Prime-Involved Exponential Diophantine Equations of the form ax ± by = z2n, Master's Thesis.
  11. • Mina, Renz Jimwel S. (2020). On Exponential Diophantine Equations of the form px +qy = zn, Master's Thesis.
  12. • Aquino, Ronald L. (2019). On Solving Diophantine Equations of the form px +qy = z3, Master's Thesis.
  13. • Antalan, John Rafael M. (2017). On Solving The Even Almost Perfect Number Problem: Some Approaches and Some New Results, Master's Thesis.
  14. • 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.

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