NONE 20260710100656660 wseas/wseas content-registration-form@crossref.org content-registration-form International Journal of Applied Mathematics Computational Science and Systems Engineering 2766-9823 Orhan Ami̇rov Faculty of Science Department of Mathematics, Ataturk University, Erzurum, TURKEY Sherif Ami̇rov Faculty of Science Department of Mathematics, Karabuk University, Karabuk, TURKEY In this study, two different methods are presented for generating Pythagorean triples. Furthermore, based on the obtained results, it is mathematically demonstrated that one element of a Pythagorean triple is always a multiple of 4, another is always a multiple of 5, and in certain special cases, one of the elements is a multiple of 20. 07 10 2026 07 10 2026 39 3 https://creativecommons.org/licenses/by/4.0/deed.en_US 10.37394/232026.2026.8.3 https://wseas.com/journals/amcse/2026/a06amcse-003(2026).pdf L. P. Fibonacci, Liber Quadratorum, 1225. L. P. Fibonacci, The Book of Squares (Liber Quadratorum): An Annotated Translation into Modern English, translated by L. E. Sigler, Orlando, FL: Academic Press, 1987. ISBN 978-0126431308. M. Stifel, Arithmetica Integra, 1544. J. Ozanam, Recreations in Mathematics and Natural Philosophy, Vol. 1, G. Kearsley, 1814, p. 49. Retrieved November 19, 2009. L. E. Dickson, History of the Theory of Numbers, Vol. II: Diophantine Analysis, Carnegie Institution of Washington, Publication No. 256, 1920, 12 + 803 pp. (Read online – University of Toronto). H. L. Price, “The Pythagorean Tree: A New Species,” arXiv preprint, arXiv:0804.4324 [math.HO], 2008. B. Berggren, “Pytagoreiska trianglar,” Tidskrift för Elementar Matematik, Fysik och Kemi, vol. 17, pp. 129–139, 1934. A. Carvalho and C. Pereira dos Santos, “A Very Useful Pythagorean Tree,” in Proceedings of the Recreational Mathematics Colloquium II, J. N. Silva, Ed., University of Évora, Portugal, Apr. 27–30, 2011, pp. 3–15. Lisboa: Associação Ludus, 2012. ISBN 9789899734623. R. Amato, “A Characterization of Pythagorean Triples,” JP Theory and Applications Journal of Algebra, vol. 39, no. 2, pp. 221–230, 2017. DOI: 10.17654/NT039020221 J. L. Poet and D. L. Vestal Jr., “Curious Consequences of a Miscopied Quadratic,” The College Mathematics Journal, vol. 36, pp. 273–277, 2005. DOI: 10.1080/07468342.2005.11922139 E. Barbeau, Power Play, Mathematical Association of America, p. 151, item 3, 1997. DOI: 10.1090/spec/092 P. Wade and W. Wade, “Recursions that Produce Pythagorean Triples,” The College Mathematics Journal, vol. 31, no. 2, pp. 98–101, Mar. 2000. DOI: 10.1080/07468342.2000.11974121 D. McCullough and E. Wade, “Recursive Enumeration of Pythagorean Triples,” The College Mathematics Journal, vol. 34, no. 2, pp. 107–111, Mar. 2003. DOI: 10.1080/07468342.2003.11921992