SOME RESULTS ON SEVERAL NUMBERICAL P+53 SETS

Year 2021, Volume: 4 Issue: 2, 1 - 6, 02.06.2021

Özlem Çelik , Murat Eren

Abstract

Diophantine set theory has an importence role in Mathematics.In this paper,we consider prime number p=+53 and give some Diophantine P+53 triples. Some of the such sets are extended but others not. We give several of them with proofs. Also, some types of elements of the Diophantine P+53 m-tubles are determined. One can be work on other Diophantine P+53 - m tubles and discover extendibility of them.

Keywords

Diophantine Ps 3-Tuple, Number Theory, Elements of Diophantine Ps m-tuples

Supporting Institution

Kırklareli Üniversitesi

Project Number

KLUBAP-213

Thanks

First of all we would like to thank Assoc. Prof. Dr. Özen Özer for her gentle guidance and strong support. We also would like to thank Kırklareli University for support the project KLUBAP-213.

References

• 1. Cohen H. (2007). Number Theory vol.1. Tools and diophantine equations, Springer.
• 2. Dudek A.W. (2016). On The number of divisors of n2 -1 ,Bull. Aust. Math. Soc. 93 194-198.
• 3. Dujella A. (2002). On the size Diophantine m-tubles, Math. Proc. Cambridge Philos Soc.132,23-33
• 4. Dujella A. (2016). What is a Diophantine m-tuple?, Notices Amer. Math. Soc.63 , 772-774.
• 5. Dujella A., Petricevic, V. (2019). On the largest element in D(n)- quadruples, Indag. Math. (N.S.) 30 1079-1086.
• 6. Earp-Lynch S. (2019). Diophantine Triples and Linear Forms in Logarithms, Master Thesis, Brock University.
• 7. Filipin, A. and Jurasic A. (2016). On the size of diophantine m-tubles for linear polynomials, Miskolc Math.Notes 17, 861-876
• 8. Gopalan M.A., Vidhyalaksfmi S., Özer Ö., (2018). A Collection of Pellian Equation ( Solutions and Properties) , Akinik Publications, New Delh, INDIA.
• 9. Gopalan M.A., Thangam S.A., Özer Ö., (2020) On The Quinary Homogeneous Bi-Quadratic Equation, Journal of Fundamental and Applied Sciences (JFAS), 2020, 12(2), 516-524.
• 10. Izadi F., Khoshnam F. (2014). On ellipticcurves via Heron Triangles and Diophantine triples, J.Math.Ext.8 17-26
• 11. Larson D. And CantuJ., (2015). Parts 1 and II of the Law of Quadratic Reciprocity, Texas A&M Universty, Lecture Notes.
• 12. Mollin R.A., (2008). Fundamental Number Theory with Applications,CRC Press.
• 13. Rihane E.A., Hernane M.O., Togbe, A. (2019). On Diophantine triples of Pell numbers, Collog. Math. 156,273-285.
• 14. Rihane A., Hernane M.O., Togbe, A. (2019).On Diophantine Triples of Pell numbers, Collog. Math. 156, 273-285.
• 15. Özer Ö., (2016). A Note On The Particular Sets With Size Three, Boundary Field Problems and Computer Simulation Journal,55: 56-59.
• 16. Özer Ö., (2017). Some Properties of The Certain Pt Sets International Journal of Algebra and Statistics, 6 (1-29) ;117-130.
• 17. Özer Ö., (2018). On The Some Nonextandable Regular P -2 Sets , Malaysian Journal of Mathhematical Sciences, 12(2): 255-266.
• 18. Özer Ö., (2019). Some Results on Especial Diophantine Sets With Size-3 JAMAME Vol :2, No:1,1-11
• 19. 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 20. 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.
• 21. Özer Ö., Sahin Z.C. (2018). On some particuler reguler Diophantine 3-truples , Math. Nat.Sci. 3, 29-38
• 22. Özer Ö. (2019). Some Results on espacial Diophantine sets with size 3, Journal of Advenced Mathematics and Mathematic Education 2, 1-11.
• 23. Silverman, J. H., (2013). A Friendly Introduction to number Theory. 4th Ed. Upper Saddle River: Pearson, 141-157.
• 24. Trudgian T.S. (2015). Bounds on the number of Diophantine quintubles, J. Number Theory 157 8, 233-249.
• 25. 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, No.3, 65-71, DOI:10.7546/NNTDM.2019.25.3.65-71.