ON THE STRUCTURE OF SOLUTIONS NO A LINEAR DIOPHANTINE EQUATION
DOI:
https://doi.org/10.52754/16948645_2024_1(4)_36Keywords:
Diophantine equation, greatest common divisor, linear combinations, sets, abelian groupAbstract
The theory of solving such equations is a classical branch of mathematics. It does not have to write complex and cumbersome formulas, but it is necessary to carry out accurate reasoning based on certain concepts of number theory, connected into a coherent logical construction. Within the framework of this theory, it is possible to give an exhaustive solution to the considered class of problems with a clearly described algorithm for obtaining an answer. These are the characteristics of a good mathematical theory.
The note contains solutions to a linear Diophantine equation in n unknowns. They are built constructively. The structural structure of these solutions is also revealed.
References
Мальцев А. И. Алгебраические системы. М.: Наука, 1970. – 392 с.
Ляпин Е. С., Евсеев А. Е. Алгебра и теория чисел. М. «Просвещение», 1974 – 383 с.
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