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Some Ps Diophantine Triples for Especial s Integer
Published Online : 29 FEB 2020
Article Views: 35 | Article Download: 14  Full PDF


The aim of this research paper is to consider some P_s –Diophantine triples including integer numbers under the special condition for s=55. It is demonstrated that they can not be extended to P_55 –Diophantine quadruples but they are regular. Also, several properties on the elements of this type sets are obtained. Some notations such as Modular Arithmetic, Quadratic Reciprocity or Residue Law, Legendre Symbol are used to prove our results.
Keywords : Diophantine m-Tuples, P_s Diophantine Triple, Quadratic Residue and Reciprocity Law, Legendre Symbol, Prime Factorization


Cohen, H. (2007). Number Theory vol.1. Tools and diophantine equations, Springer. Dujella, A. (2002). On the size of Diophantine m-tuples, Math. Proc. Cambridge Philos. Soc. 132, 23-33. Dujella, A., (2016). What is a Diophantine m-tuple?, Notices Amer. Math. Soc. 63 , 772-774. Gopalan M.A., Vidhyalaksfmi S. , Özer Ö., (2018). A Collection of Pellian Equation (Solutions and Properties), Akinik Publications, New Delhi, INDIA. Gopalan, M.A. Thangam, S., Özer, Ö. (2019), On the System of Double Equations with Three Unknowns , International Journal of Nonlinear Analysis and Applications, DOI: 10.22075/IJNAA.2019.14412.1757 , Articles in Press. Larson, D. and Cantu J., Parts I and II of the Law of Quadratic Reciprocity, Texas A&M University, Lecture Notes, 2015. Mollin R.A., Fundamental Number Theory with Applications, CRC Press, 2008. Özer Ö., (2016). A Note On The Particular Sets With Size Three, Boundary Field Problems and Computer Simulation Journal, 55: 56-59. Özer Ö.,(2016). On The Some Particular Sets, Kırklareli University Journal of Engineering and Science, 2: 99-108. Özer Ö., (2017). Some Properties of The Certain Pt Sets, International Journal of Algebra and Statistics, 6 (1-2) ;117-130. Özer Ö., (2018). On The Some Nonextandable Regular P_(-2) Sets , Malaysian Journal of Mathematical Sciences, 12(2): 255–266. Özer Ö., (2019). Some Results on Especial Diophantine Sets with Size-3, JAMAME, Vol:2,No:1, 1-11. Özer Ö., (2019), A Certain Type of Regular Diophantine Triples and Their Non-Extendability, Turkish Journal of Analysis & Number Theory, 2019, 7(2), 50-55. DOI: 10.12691/tjant-7-2-4. Özer Ö., Gopalan M.A., (2019). On the homogeneous cone, Pioneer Journal of Mathematics and Mathematical Sciences (PJMMS), Volume 25, Issue 1, Pages 9-18. Rihane, E.A., Hernane, M.O., Togbe, A. (2019), On Diophantine triples of Pell numbers, Colloq. Math. 156, 273-285. Silverman, J. H., A Friendly Introduction to Number Theory. 4th Ed. Upper Saddle River: Pearson, 141-157, 2013. Vidhyalakshmi, S., Gopalan, M.A., Thangam, S., Özer, Ö., (2019). On the Ternary Biquadratic Diophantine Equation, Notes on Number Theory and Discrete Mathematics, Vol. 25, 2019, No. 3, 65–71, DOI: 10.7546/nntdm.2019.25.3.65-71.
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