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Year 2020, , 86 - 92, 22.06.2020
https://doi.org/10.32323/ujma.641744

Abstract

References

  • [1] M. Clausen, A. Fortenbacher, Efficient solution of linear diophantine equations, J. Sym. Comp., 8(1-2) (1989), 201–216.
  • [2] E. Contejean, H. Contejean, An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations, Inf. Comp., 113(1) (1994), 143–172.
  • [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] V. Y. Nesterenko, Number Theory. ”Academy”, Moscow (in Russian), 2008.
  • [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.
  • [6] A. Vigneron-Tenorio, Semigroup ideals and linear diophantine equations, Linear Algebra Appl., 295(1999), 133–144

On Some Methods for Solution of Linear Diophantine Equations

Year 2020, , 86 - 92, 22.06.2020
https://doi.org/10.32323/ujma.641744

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.

References

  • [1] M. Clausen, A. Fortenbacher, Efficient solution of linear diophantine equations, J. Sym. Comp., 8(1-2) (1989), 201–216.
  • [2] E. Contejean, H. Contejean, An Efficient Incremental Algorithm for Solving Systems of Linear Diophantine Equations, Inf. Comp., 113(1) (1994), 143–172.
  • [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] V. Y. Nesterenko, Number Theory. ”Academy”, Moscow (in Russian), 2008.
  • [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.
  • [6] A. Vigneron-Tenorio, Semigroup ideals and linear diophantine equations, Linear Algebra Appl., 295(1999), 133–144
There are 6 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Azam Imomov 0000-0003-1082-0144

Yorqin T. Khodjaev This is me

Publication Date June 22, 2020
Submission Date November 2, 2019
Acceptance Date June 17, 2020
Published in Issue Year 2020

Cite

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 Imomov A, Khodjaev YT. On Some Methods for Solution of Linear Diophantine Equations. Univ. J. Math. Appl. June 2020;3(2):86-92. doi:10.32323/ujma.641744
Chicago Imomov, Azam, and Yorqin T. Khodjaev. “On Some Methods for Solution of Linear Diophantine Equations”. Universal Journal of Mathematics and Applications 3, no. 2 (June 2020): 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 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, 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 2020), 86-92. https://doi.org/10.32323/ujma.641744.
JAMA 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, 2020, pp. 86-92, doi:10.32323/ujma.641744.
Vancouver Imomov A, Khodjaev YT. On Some Methods for Solution of Linear Diophantine Equations. Univ. J. Math. Appl. 2020;3(2):86-92.

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