Diophantine equations

Authors

  • Sirichan Vesarachasart Thammasat University
  • Wanitcha Chomcherd Thammasat University
  • Kevalin Yeesan Thammasat University

Keywords:

Diophantine equation, Non-negative integer solution, Prime number

Abstract

In this paper, we are interested to study two Diophantine equations gif.latex?p^4+2q^4=z^2and gif.latex?p^4-2q^4=z^2 where p,q are prime numbers. The results of this study, we found that the Diophantine equation gif.latex?p^4-2q^4=z^2 has only one non-negative integer solution, that is gif.latex?(p,q,z)=(3,2,7) for the Diophantine equationgif.latex?p^4+2q^4=z^2 has no solution.

Author Biographies

Sirichan Vesarachasart, Thammasat University

Department of Mathematics and Statistics, Faculty of Science and Technology

Wanitcha Chomcherd, Thammasat University

Department of Mathematics and Statistics, Faculty of Science and Technology

Kevalin Yeesan, Thammasat University

Department of Mathematics and Statistics, Faculty of Science and Technology

References

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Rabago, J.F.T., (2013). On two Diophantine equations and . Int. J. Math. Sci. Comput., 3(1), (28-29).

Burshtein, N. (2018). On Solutions to the Diophantine Equations . Pure Appl. Math., 18(1), (79-81).

Burshtein, N.(2018).On Solutions of the Diophantine Equations and when and are Primes. Pure Appl. Math., 18(1), (51-57).

Burshtein, N.(2018).On Solutions of the Diophantine Equations and when and are Primes. Pure Appl. Math., 19(1), (1-5).

Burshtein, N. (2017). On solution of the Diophantine equation . Ann. Pure Appl. Math., 13, (143-149).

Vesarachasart S., Sakornthai K., Phumiphong N. and Lueangsubthawee W. (2019). All Solutions of the Diophantine equation where and are Prime numbers. Thai Journal of Science and Technology, 9(2), (207-210).

Patthanangkoor, T. (2007). Elementary of number theory. Pathum Thani: Thammasat University Press.

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Published

2023-08-31

How to Cite

Vesarachasart, S., Chomcherd , W., & Yeesan, K. (2023). Diophantine equations. SciTech Research Journal, 6(2), 34–40. Retrieved from https://ph02.tci-thaijo.org/index.php/jstrmu/article/view/250173

Issue

Section

Research Articles