Fundamentalnaya i Prikladnaya Matematika
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor
Journal history

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Fundam. Prikl. Mat.:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Fundamentalnaya i Prikladnaya Matematika, 2000, Volume 6, Issue 3, Pages 649–668 (Mi fpm496)  

This article is cited in 1 scientific paper (total in 1 paper)

Exponential Diophantine equations in rings of positive characteristic

A. Ya. Belova, A. A. Chilikovb

a House of scientific and technical work of youth
b M. V. Lomonosov Moscow State University
Full-text PDF (799 kB) Citations (1)
Abstract: In this work we prove the algorithmical solvability of the exponential-Diophan-tine equations in rings represented by matrices over fields of positive characteristic. Consider the system of exponential-Diophantine equations
$$ \sum_{i=1}^{s}P_{ij}(n_1,\ldots,n_t)b_{ij0}a_{ij1}^{n_1}b_{ij1}\ldots a_{ijt}^{n_t}b_{ijt}=0 $$
where $b_{ijk},a_{ijk}$ are constants from matrix ring of characteristic $p$, $n_i$ are indeterminates. For any solution $\langle n_1,\ldots,n_t \rangle$ of the system we construct the word (over alphabet which contains $p^t$ symbols) $\overline\alpha_0\ldots\overline\alpha_q$, where $\overline\alpha_i$ is a $t$-tuple $\langle n_1^{(i)},\ldots,n_t^{(i)}\rangle$, $n^{(i)}$ is the $i$-th digit in the $p$-adic representation of $n$. 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 (i. e. recognizible by a finite automaton). There is an effective algorithm which calculates this language.
Received: 01.03.1998
Bibliographic databases:
UDC: 512.5+511
Language: Russian
Citation: A. Ya. Belov, A. A. Chilikov, “Exponential Diophantine equations in rings of positive characteristic”, Fundam. Prikl. Mat., 6:3 (2000), 649–668
Citation in format AMSBIB
\Bibitem{BelChi00}
\by A.~Ya.~Belov, A.~A.~Chilikov
\paper Exponential Diophantine equations in rings of positive characteristic
\jour Fundam. Prikl. Mat.
\yr 2000
\vol 6
\issue 3
\pages 649--668
\mathnet{http://mi.mathnet.ru/fpm496}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1801320}
\zmath{https://zbmath.org/?q=an:0990.11079}
Linking options:
  • https://www.mathnet.ru/eng/fpm496
  • https://www.mathnet.ru/eng/fpm/v6/i3/p649
  • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Фундаментальная и прикладная математика
    Statistics & downloads:
    Abstract page:570
    Full-text PDF :183
    First page:1
     
      Contact us:
     Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2024