On the Non-Linear Diophantine Equation 331x +349y =z2

  • Sudhanshu Aggarwal Assistant Professor, Department of Mathematics, National PG College, Barhalganj, Gorakhpur, Uttar Pradesh, India. http://orcid.org/0000-0001-6324-1539
  • Swarg Deep Sharma Assistant Professor, Department of Mathematics, Nandlal Singh College, Jaitpur (Constituent of Jai Prakash University, Ch- hapra), Bihar, India.
  • Raman Chauhan Assistant Professor, Noida Institute of Engineering and Technology, Greater Noida, Uttar Pradesh, India.

Abstract

Authors discussed the existence of solution of non-linear Diophantine equation 331x+349y=z2, where x, y, z are non-negative integers, in this paper. Results of paper show that the non-linear Diophantine equation 331x+349y=z2, where x, y, z are non-negative integers, has no non-negative integer solution.


How to cite this article: Aggarwal S, Sharma SD, Chauhan R. On the Non-Linear Diophantine Equation 331x+349y=z2. J Adv Res Appl Math Stat 2020; 5(3&4): 6-8.


Mathematics Subject Classification: 11D61, 11D72, 11D45.

References

1. Acu D. On a Diophantine equation 2x+5y=z2. General Mathematics 2007; 15(4), 145-148.
2. Kumar S, Gupta S, Kishan H. On the non-linear Diophantine equations 61x+67y=z2 and 67x+73y=z2. Annals of Pure and Applied Mathematics 2018; 18(1): 91-94.
3. Kumar S, Gupta D, Kishan H. On the non-linear Diophantine equations 31x+41y=z2 and 61x+71y=z2. Annals of Pure and Applied Mathematics 2018; 18(2): 185-188.
4. Mordell LJ. Diophantine equations, Academic Press, London, NewYork 1969.
5. Rabago JFT. On an open problem by B. Sroysang. Konuralp Journal of Mathematics 2013; 1(2): 30-32.
6. Sierpinski W. Elementary theory of numbers, Warszawa 1964.
7. Sroysang B. More on the Diophantine equation 8x+19y=z2. International Journal of Pure and Applied Mathematics 2012; 81(4): 601-604.
8. Sroysang B. On the Diophantine equation 8x+13y=z2. International Journal of Pure and Applied Mathematics. 2014; 90(1): 69-72.
9. Sroysang B. On the Diophantine equation 31x+32y=z2. International Journal of Pure and Applied Mathematics, 81(4): 609-612.
10. Aggarwal S, Sharma SD, VyasA. On the existence of solution of Diophantine equation 181x+199y=z2. International Journal of Latest Technology in Engineering, Management & Applied Science 2020; 9(8): 85-86.
11. Aggarwal S, Sharma SD, Singhal H. On the Diophan-tine equation 223x+241y=z2. International Journal of Research and Innovation in Applied Science 2020; 5(8): 155-156.
Published
2020-12-30
How to Cite
AGGARWAL, Sudhanshu; SHARMA, Swarg Deep; CHAUHAN, Raman. On the Non-Linear Diophantine Equation 331x +349y =z2. Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 5, n. 3&4, p. 6-8, dec. 2020. ISSN 2455-7021. Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/4>. Date accessed: 02 jan. 2025.
Citation Formats
Issue
Vol 5 No 3&4 (2020): Journal of Advanced Research in Applied Mathematics and Statistics
Section
Articles