Some Results on Especial Diophantine Sets with Size-3

Yıl 2019, Cilt: 2 Sayı: 1, 1 - 11, 01.01.2019

Özen Özer

Öz

Purpose of this paper is to determine some regular non-extendible D n triples for some fixed integer n. Besides, paper includes a number of algebraic properties for such diophantine sets with size three

Anahtar Kelimeler

Diophantine Sets, Property D n, Integral Solutions of Pell Equations

Kaynakça

• Gopalan M.A., Vidhyalaksfmi S. , Özer Ö., “A Collection of Pellian Equation (Solutions and Properties)”, Akinik Publications, New Delhi, INDIA, 2018.
• Ireland K. and Rosen M., A Classical Introduction to Modern Number Theory, 2nd ed., Graduate Texts in Mathematics,vol. 84, Springer-Verlag, New York, 1990.
• Jimbo, H.C. and Ngongo, I.S., Application of Limit Theorem to sum of Legendre Symbols, Acta Math. Univ. Comenianae, Vol. (submitted to AMUC), pp. 1-5.
• Kohnen, W., An Elemenary Proof in the Theory of Quadratic Resıdues, Bull. Korean Math. Soc. 45 (2008), No. 2, pp. 273-275.
• Lemmermeyer, F. Reciprocity Laws: from, Euler to Eisenstien. Berlin Hiedelberg New York: Springer-Verlag,2000.
• Mathmdmb, Primitive Roots,Order, Quadratic Residue, Lecture Notes, March 30, 2011.
• Mollin R.A., Fundamental Number theory with Applications, CRC Press, 2008.
• Özer Ö., A Note On The Particular Sets With Size Three, Boundary Field Problems and Computer Simulation Journal, 55, 56-59, 2016.
• Özer Ö., On The Some Particular Sets, Kırklareli University Journal of Engineering and Science, 2, 99-108, 2016.
• Özer Ö., Some Properties of The Certain Pt Sets, International Journal of Algebra and Statistics, Vol. 6; 1-2 , 117-130, 2017.
• Özer Ö., On The Some Nonextandable Regular |L Sets, Malaysian Journal of Mathematical Sciences 12(2): 255–266, 2018.
• Özer Ö., Dubey O.P., On Some Particular Regular Diophantine 3-Tuples, Mathematics in Natural Sciences, (Accepted).
• Stillwell, J. Elements of Number Theory. New York: Springer-Verlag, 2003.