Bulletin KRASEC. Phys. & Math. Sci. 2016. V. 13. no. 2. pp. 16-21. ISSN 2313-0156

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DOI: 10.18454/2313-0156-2016-13-2-16-21

MSC 34L99

LINEAR DIOPHANTINE EQUATIONS AND WAYS TO SOLVE THEM

A. Kh. Kodzokov, Z. O. Beslaneev, A. L. Nagorov, M. B. Tkhamokov

Kabardino-Balkarian state university of H.M. Berbekov 360004, KBR, Nalchik, Chernyshevsky str., 173
E-mail: kodzoko@mail.ru

The paper discusses the ways to solve linear Diophantine equations both in a special case with two unknown quantities, and in a general case with few unknowns. The main result is contained in Theorem 1, which assumes the general method to solve any Diophantine equation based on the congruence modulo.

Key words: linear Diophantine equations, congruence modulo, Euclidean algorithm method.

 

References

  1. Bashmakova I. G. Diofant i diofantovy uravneniya [Diophant and Diophantine equations]. Moscow. Nauka. 1972. 68 p.
    2. Solov’ev Yu. N. Neopredelennye uravneniya pervoy stepeni [Undetermined equations of the first degree]. Kvant – Quantum. 1992. no. 4. 42–46.
    3. Bukhshtab A. A. Teoriya chisel [Theory of numbers]. Moscow. Prosveshchenie. 1966. 385 p.
    4. Serpinskiy V. O reshenii uravneniy v tselykh chislakh [On the solution of equations in integral numbers]. Moscow. Fizmatlit. 1961. 88 p.

For citation: Kodzokov A. Kh., Beslaneev Z. O., Nagorov A. L., Tkhamokov M. B. Linear Diophantine equations and ways to solve them. Bulletin KRASEC. Physical and Mathematical Sciences 2016, vol. 13, no 2, 16-21. DOI: 10.18454/2313-0156-2016-13-2-16-21.

Original article submitted: 29.03.2016

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    Kodzokov Azamat Khasanovich – Senior Lecturer, Dep. of Mathematical Analysis and Function Theory, KabardinoBalkarian state university of H.M. Berbekov, Nalchik, Republic of KabardinoBalkaria, Russia.

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 Beslaneev Zalimbek Olegovich – High teacher of IMOAS chair, KabardinoBalkarian state university of H.M. Berbekov, Nalchik, Republic of KabardinoBalkaria, Russia.

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    Nagorov Aslan L’vovich – High teacher of IMOAS chair, Kabardino-Balkarian state university of H.M. Berbekov, Nalchik, Republic of KabardinoBalkaria, Russia.

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  Tkhamokov Muslim Bashirovich – Senior Lecturer, Department of Computational Mathematics, Kabardino-Balkarian state university of H.M. Berbekov, Nalchik, Republic of KabardinoBalkaria, Russia.

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