Diophantine quadruples of numbers whose elements are in proportion

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Published: Sep 30, 2017
DOI: https://doi.org/10.5556/j.tkjm.48.2017.1972
Keywords:
P3 k sequence Recurrence relation Diophantine quadruples Pell's equation

Main Article Content

A.M.S. Ramasamy

Abstract

In this paper certain non-F-type $P_{3,k}$ sequences which contain Diophantine quadruples of numbers in proportion are presented. It is proved that there exist an infinite number of non-F-type $P_{3,k}$ sequences which possess Diophantine quadruples of numbers in proportion.

Article Details

How to Cite
Ramasamy, A. (2017). Diophantine quadruples of numbers whose elements are in proportion. Tamkang Journal of Mathematics, 48(3), 241–249. https://doi.org/10.5556/j.tkjm.48.2017.1972
Issue
Vol. 48 No. 3 (2017)
Section
Papers
Author Biography

A.M.S. Ramasamy

Department ofMathematics, Vel Tech Dr. RR & Dr. SR Technical University, Avadi, Chennai - 600062, India.

References

A.Baker and H.~Davenport, The equations $3x^2 - 2 = y^2$ and $8x^2 - 7 = z^2$, Quart.J.Math.Oxford, 20(1969),129--137.

A.Dujella, On Diophantine quintuples,Acta Arith., 81(1997),69--70.

A.Dujella, Diophantine quadruples and quintuples modulo 4, Number Theory Discrete Math. 4(1998),160--164.

A.Dujella and A.M.S. Ramasamy, Fibonacci numbers and sets with the property D(4),Bulletin of Belgian Mathematical Society Simon Stevin,12(2005),401--412.

A.Dujella and N.~Saradha, Diophantine m-tuples with elements in arithmetic progressions, Indag.Math.(N.S.), 25(2014),131--136.

M.Gardner, Mathematical games, Scientific American,214(1967), 119pp.

S.P.Mohanty and A.M.S.Ramasamy, The simultaneous Diophantine equations $5y^2-20=x^2$ and $2y^2+1=z^2 $,Journal of Number Theory,18(1984),356--359.

S.P.Mohanty and A.M.S.~Ramasamy, On $P_{r,k}$ sequences, Fibonacci Quart., 23(1985),36--44.

S.P.Mohanty and A.M.S.Ramasamy, The characteristic number of two simultaneous Pell's equations and its application, Simon Stevin, 59(1985),203--214.

T.Nagell, Introduction to Number Theory, Wiley,New York,1951.

A.M.S.~Ramasamy,A remarkable sequence,Banyan Mathematical Journal, 2(1995),69--76.

A.M.S.Ramasamy, Sets, sequences and polynomials linked with a question of Diophantus,Bulletin of Kerala Mathematics Association,4(2007),109--125.

A.M.S.Ramasamy and D.Saraswathy,A non-extendable Diophantine quadruple arising from a triple of Lucas numbers, Involve,5(2012),257--271.

J.Roberts, Lure of the Integers,The Mathematical Association of America, Washington D.C.,1992.