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Year 2020, Volume: 3 Issue: 2, 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, Volume: 3 Issue: 2, 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 Volume: 3 Issue: 2

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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