Rational Diophantine Quadruples

M.A.Gopalan; V.Geetha

doi:https://doi.org/10.14445/22315373/IJMTT-V12P509

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 12 | Number 1 | Year 2014 | Article Id. IJMTT-V12P509 | DOI : https://doi.org/10.14445/22315373/IJMTT-V12P509

Rational Diophantine Quadruples

M.A.Gopalan, V.Geetha

Abstract

This paper concerns with the study of constructing strong rational diophantine quadruples with suitable property.

Keywords

Strong Diophantine quadruples, Pythagorean equation

References

1) J.Arkin., V.E.Hoggatt and E.G.Straus, On Euler’s solution of a problem of Diophantus, Fibonacci Quart. 17(1979), 333-339.
2) J.Arkin, D.C.Arney, F.R.Giordano, R.A.Kolb and G.E.Bergaum, An extension of an old classical Diophantine problem problem, Applications of Fibonacci Numbers, Kluwer Acad. Publ. Dorrecht, (1993), 45 -48.
3) A.Baker and H.Davenport, The equations and , Quart. J.Math. Oxford Ser., 20(2)(1969), 129-137.
4) L.E.Dickson, history of theory of numbers, Vol.2, Chelesa, New York, 1966, 513-520.
5) Diophantus of Alexandria, Arithmetics and the book of polygonal numbers, (I.G.Bashmakova, Ed.), Nauka, Moscow, 1974 (in Russia) 103 -104, 232.
6) A.Dujella, The problem of the extension of a parametric family of Diophantine triples, Publ. Publ.Math.Derbeen, 51(1997), 311-322.
7) A.Dujella and A.Petho, A generalization of a theorem of Baker and Davenport, Quart.J.Math.Oxford Ser. 49(2)(1998), 291-306.
8) A.Dujella and C.Fuchs, Complete solutions of the polynomial version of a problem of Diophantus, J.Number theory, 106(2004), 326-344.
9) A.Dujella and Vinko Petricevie, Strong Diophantine triples, Experimental Math., 17, (1), (2008).
10) A.Flipin and Fujita.Y., The triple with k prime, Glas. Mat.Ser. III46(2011), 311 -323.
11) Y.Fujita, The extensibility of Diophantine pairs , J.Number theory, 128, (2008), 322 -353.
12) Y.Fujita, Exension of the - triple , Period.Math. Hungarica, 59(2009), 81-98.
13) P.E.Gibbs, Computer Bulletin, 17 (1978), 16.
14) T.L.Heath, Diophantus of Alexandria: A study in the History of Greek Algebra, Dover Publications, Inc., New York, 1964.
15) M.A.Gopalan and G.Srividhya (2009), Diophantine Qudrapules for Fibonacci numbers with property D(1), Indian Journal of Mathematics and mathematical Sciences, 5 (2), 57-59.
16) M.A.Gopalan and G.Srividhya (2010), Diophantine Qudrapules for Pell numbers with property D(1), Antarctica Journal of Mathematics, 7(3), 357-362.
17) M.A.Gopalan and V.Pandichelvi (2011), Construction of the Diophantine triple involving Polygonal numbers, Impact J.Sci.Tech., 5(1), 7-11.
18) M.A.Gopalan and G.Srividhya (2012), Two special Diophantine Triples, Diophntus J.Math.,1(1), 23-37.
19) M.A.Gopalan, K.Geetha and Manju Somanath (2014), On special Diophantine Triple, Archimedes Journal of Mathematics, 4(1), 37-43.
20) M.A.Gopalan, V.Sangeetha and Manju Somanath (2014), Construction of the Diophantine polygonal numbers, Sch. J.Eng. Tech. 2, 19 -22.

Citation :

M.A.Gopalan, V.Geetha, "Rational Diophantine Quadruples," International Journal of Mathematics Trends and Technology (IJMTT), vol. 12, no. 1, pp. 58-62, 2014. Crossref, https://doi.org/10.14445/22315373/IJMTT-V12P509