On the Non-Linear Diophantine Equation 313x +331y =z2
Abstract
In this article, authors discussed the existence of solution of non-linear Diophantine equation 313x +331y =z2 where x, y, z are non-negative integers. Results show that the consider non-linear Diophantine equation of study has no non-negative integer solution.
How to cite this article: Aggarwal S, Sharma SD, Sharma N. On the Non-Linear Diophantine Equation 313x +331y =z2. J Adv Res Appl Math Stat 2020; 5(3&4): 3-5.
Mathematics Subject Classification: 11D61, 11D72, 11D45.
References
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11. Aggarwal S, Sharma SD, Singhal H. On the Diophantine equation 223x+241y=z2. International Journal of
Research and Innovation in Applied Science 2020; 5(8): 155-156.
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 2012; 81(4): 609-612.
10. Aggarwal S, Sharma SD, Vyas A. 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 Diophantine 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; SHARMA, Nidhi.
On the Non-Linear Diophantine Equation 313x +331y =z2.
Journal of Advanced Research in Applied Mathematics and Statistics, [S.l.], v. 5, n. 3&4, p. 3-5, dec. 2020.
ISSN 2455-7021.
Available at: <http://thejournalshouse.com/index.php/Journal-Maths-Stats/article/view/3>. Date accessed: 09 mar. 2025.
Section
Articles
