I PRIKLADNAYA MATEMATIKA
(FUNDAMENTAL AND APPLIED MATHEMATICS)
2000, VOLUME 6, NUMBER 3, PAGES 649-668
Exponential Diophantine equations in rings of positive characteristic
A. Ya. Belov
A. A. Chilikov
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In this work we prove the algorithmical solvability of
the exponential-Diophantine equations in rings represented by
matrices over fields of positive characteristic.
Consider the system of exponential-Diophantine equations
are constants from matrix ring of characteristic , are
For any solution of the system we
construct the word (over alphabet which contains symbols)
digit in the -adic representation
The main result of this work is: the set of words,
corresponding in this sense to the solutions of the system
of exponential-Diophantine equations is a regular language
recognizible by a finite automaton).
There is an effective algorithm which calculates this language.
All articles are
published in Russian.
Last modified: December 8, 2000