SOME RESULTS ON SEVERAL NUMBERICAL P+53 SETS

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

Özlem Çelik , Murat Eren

https://izlik.org/JA34WR74BL

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.

Project Number

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.