SOME NOTES ON A GENERALIZED VERSION OF PYTHAGOREAN TRIPLES
DOI:
https://doi.org/10.26740/jram.v4n2.p103-107Keywords:
Pythagorean triple, Diophantine equation, PrimitiveAbstract
A Pythagorean triple is a set of three positive integers a, b and c that satisfy the Diophantine equation a^2+b^2=c^2. The triple is said to be primitive if gcd(a, b, c)=1 and each pair of integers and are relatively prime, otherwise known as non-primitive. In this paper, the generalized version of the formula that generates primitive and non-primitive Pythagorean triples that depends on two positive integers k and n, that is, P_T=(a(k, n), b(k, n), c(k, n)) were constructed. Further, we determined the values of k and n that generates primitive Pythagorean triples and give some important results.
References
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Shannon, A. G. & Horadam, A. F. (1973). Generalized Fibonacci number triples. <em>American Mathematical Monthly</em>, <em>80</em>(2), 187-190.
Shannon, A. G. & Horadam, A. F. (1994). Arrowhead curves in a tree of Pythagorean triples. <em>International Journal of Mathematical Education in Science and Technology</em>, <em>25</em>(2), 255-261.
Niven, I. and Zuckerman, H. S. (1980). <em>An Introduction to the theory of numbers.</em> 4<sup>th</sup> edition.<em> </em>John Wiley and Sons, Inc. Canada.
Rosen, K. H. 1993. <em>Elementary Number Theory and its Application</em>. 3<sup>rd</sup> edition. Addison-Wesley Publishing Company, USA.
Dickson, L. E. (1971). <em>History of the Theory of Numbers</em>. Chelsea Pub. Co., New York.
Erickson, M. and Vazzana, A. (2008). <em>Introduction to Number Theory. </em>Taylor and Francis Group, New York, USA.
Casinillo. L. F. (2020). Some new notes on Mersenne primes and perfect numbers. <em>Indonesian Journal of Mathematics Education, 3</em>(1), 15-22.
Casinillo, L. F. (2020). Odd and even repetition sequences of independent domination number. <em>Notes on Number Theory and Discrete Mathematics, 26</em>(1), 8-20.
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Published
21-10-20
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Combinatorics and Computational Mathematics
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