SOLUTIONS OF THE DIOPHANTINE EQUATION 15^x+4^y=z^2

  • Abhiwat Kambheera
  • Kiattisak Kumpapan Phetchabun Rajabhat University
Keywords: Diophantine equation, Solution, Catalan's type

Abstract

In this paper, we study solutions of the Diophantine equation 15x+4y=zhas a unique non-negative integers. We found that this equation has solution exactly     (x, y,z) = (1, 0, 4) 

Downloads

Download data is not yet available.

References

Acu D. On a diophantine equation . General Mathematics. 2007; 15(4);
145-148.
Andrew Goerge E. Number Theory. Philadephia : W.B. Saunders. 1971.
David MB. Elementary Number Theory. 6th ed. Singapore: McGraw-Hill. 2007.
Kenneth HR. Elementary Number Theory and its Application. 4th ed. Addison Wesley
Longman, Inc. 2000.
Khunpanuk C. Number Theory. Phetchabun: Phetchabun Coppyceter; 2014; 175-189.
LeVeque WMJ. On the equation . American Journal of Mathematics. 1952; 74: 325-331.
Mihailescu P. Primary cyclotomic units and a proof of Catalan's conjecture. Journal Reine Angew Math. 2004; 27: 167-195.
Mordell LJ. Diophantine Equations. New York: Academic Press; 1969.
Punnim N and Prapaphot N. Number Theory. Bankkok: The Promotion of Academic Olympiad and Development of Science Education Foundation under the patronage of Her Royal Highness Princess Galyani Vadhana Krom Luang Naradhiwas Rajanagarindra; 2004: 169-195.
Silverman JH. A Friendly Introduction to Number Theory. 2nd ed. New Jersey: Prentice-Hall, Inc; 2001.
Sandor J. On a diophantine equation . Geometric theorems, Diophantine equations, and arithmetric functions. American Research Press Rehobot 4. 2002; 89-90.
Sandor J. On a diophantine equation , Geometric theorems, Diophantine equations, and arithmetric functions, American Research Press Rehobot 4. 2002; 91-92.
Sierpinski W. Elementary Theory of Numbers. Warszawa. 1964.
Suvarnamani A, Singta A, and Chotchaisthit S. On two Diophantine equations and . Science and Technology RMUTT Journal.
2011; 1(1): 25-28.
Suvarnamani A. Solution of the Diophantine equation . International Journal of Mathematical Sciences and Applications. 2011; 1(3): 1415-1419.
Published
2020-06-30
How to Cite
Kambheera, A., & Kumpapan, K. (2020). SOLUTIONS OF THE DIOPHANTINE EQUATION 15^x+4^y=z^2. Life Sciences and Environment Journal, 21(1), 255-261. Retrieved from https://ph01.tci-thaijo.org/index.php/psru/article/view/240374
Section
Research Articles