A Geometrial Approach to the Diophantine Equation

Authors

  • Warin Vipismakul Department of Mathematics, Faculty of Science, Burapha University
  • Ratchanikorn Chonchaiya Department of Mathematics, Faculty of Science, King Mongkut's University of Technology Thonburi
  • Arisa Jiratampradab Department of Statistics, Faculty of Science, Kasetsart University

Keywords:

Diophantine solutions , Pythagorean triples , unitn-sphere

Abstract

We find all Diophantine solutions for the equation  by refining the geometrical approach from (Ayoub, 1984) to find solutions of the equation  We can find all rational points on the unit n-sphere by lines connecting those rational points to the point  Such linear parametric equations will always have rational slopes.         

References

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Dainelli, U. (1877). Giornale di Mat., 15, 378.

Gill, C. (1826). The Gentleman's Math. Companion, 29(5), 364.

Dickson, L. E. (1966). History of the Theory of Numbers (Vol. 2), Chelsea Publishing.

Euler, J. A. (1779). Acta Acad. Petrop., 3, 40.

Huerlimann, W. (2002). The Primitive Cuboids with Natural Edges and Diagonals According to Catalan and Sierpinski. Mathematics Preprint Archive, 2002 (2), 444-452. (SSRN: https://ssrn.com/abstract=3133707)

Huerlimann, W. (2015). Hopf's quadratic map and permutation invariant properties of primitive cuboids, Algebra Lett., 2015, Article ID 2.

Lebesgue, V. A. (1874). Nouv. Ann. Math., 13(2), 64.

Mikami, Y. (1912). Abh. Geschichte Math. Wiss., 30, 233.

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Published

2026-03-19

How to Cite

Vipismakul, W., Chonchaiya, R., & Jiratampradab, A. (2026). A Geometrial Approach to the Diophantine Equation . Burapha Science Journal, 26(3 September-December), 1364–1370. retrieved from https://li05.tci-thaijo.org/index.php/buuscij/article/view/1356

Issue

Vol. 26 No. 3 September-December (2021): Burapha Science Journal

Section

Research Articles

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