Research Article

On Some Methods for Solution of Linear Diophantine Equations

Volume: 3 Number: 2 June 22, 2020
EN

On Some Methods for Solution of Linear Diophantine Equations

Abstract

The paper considers a linear Diophantine equation. A method (algorithm) for finding a general class of solutions of equation is proposed. The proposed algorithm is explained by examples of equations with two and three variables, trying to direct the reader to a general idea that describes the essence of the method used.

Keywords

Diophantine equation,General solution

References

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  3. [3] H. Esmaeili, How can we solve a linear Diophantine equation by the basis reduction algorithm, Int. J. Comp. Math., 82(10)(2005), 1227–1234.
  4. [4] V. Y. Nesterenko, Number Theory. ”Academy”, Moscow (in Russian), 2008.
  5. [5] D. Papp, B. Vizvari, Effective solution of linear Diophantine equation systems with an application in chemistry, J. Math. Chem., 39(1)(2006), 15–31.
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APA
Imomov, A., & Khodjaev, Y. T. (2020). On Some Methods for Solution of Linear Diophantine Equations. Universal Journal of Mathematics and Applications, 3(2), 86-92. https://doi.org/10.32323/ujma.641744
AMA
1.Imomov A, Khodjaev YT. On Some Methods for Solution of Linear Diophantine Equations. Univ. J. Math. Appl. 2020;3(2):86-92. doi:10.32323/ujma.641744
Chicago
Imomov, Azam, and Yorqin T. Khodjaev. 2020. “On Some Methods for Solution of Linear Diophantine Equations”. Universal Journal of Mathematics and Applications 3 (2): 86-92. https://doi.org/10.32323/ujma.641744.
EndNote
Imomov A, Khodjaev YT (June 1, 2020) On Some Methods for Solution of Linear Diophantine Equations. Universal Journal of Mathematics and Applications 3 2 86–92.
IEEE
[1]A. Imomov and Y. T. Khodjaev, “On Some Methods for Solution of Linear Diophantine Equations”, Univ. J. Math. Appl., vol. 3, no. 2, pp. 86–92, June 2020, doi: 10.32323/ujma.641744.
ISNAD
Imomov, Azam - Khodjaev, Yorqin T. “On Some Methods for Solution of Linear Diophantine Equations”. Universal Journal of Mathematics and Applications 3/2 (June 1, 2020): 86-92. https://doi.org/10.32323/ujma.641744.
JAMA
1.Imomov A, Khodjaev YT. On Some Methods for Solution of Linear Diophantine Equations. Univ. J. Math. Appl. 2020;3:86–92.
MLA
Imomov, Azam, and Yorqin T. Khodjaev. “On Some Methods for Solution of Linear Diophantine Equations”. Universal Journal of Mathematics and Applications, vol. 3, no. 2, June 2020, pp. 86-92, doi:10.32323/ujma.641744.
Vancouver
1.Azam Imomov, Yorqin T. Khodjaev. On Some Methods for Solution of Linear Diophantine Equations. Univ. J. Math. Appl. 2020 Jun. 1;3(2):86-92. doi:10.32323/ujma.641744