On the Diophantine equation

Amir Khosravi; Behrooz Khosravi

Commentationes Mathematicae Universitatis Carolinae (2003)

  • Volume: 44, Issue: 1, page 1-7
  • ISSN: 0010-2628

Abstract

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There exist many results about the Diophantine equation , where and . In this paper, we suppose that , is an odd integer and a power of a prime number. Also let be an integer such that the number of prime divisors of is less than or equal to . Then we solve completely the Diophantine equation for infinitely many values of . This result finds frequent applications in the theory of finite groups.

How to cite

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Khosravi, Amir, and Khosravi, Behrooz. "On the Diophantine equation $\frac{q^n-1}{q-1}=y$." Commentationes Mathematicae Universitatis Carolinae 44.1 (2003): 1-7. <http://eudml.org/doc/249149>.

@article{Khosravi2003,
abstract = {There exist many results about the Diophantine equation $(q^n-1)/(q-1)=y^m$, where $m\ge 2$ and $n\ge 3$. In this paper, we suppose that $m=1$, $n$ is an odd integer and $q$ a power of a prime number. Also let $y$ be an integer such that the number of prime divisors of $y-1$ is less than or equal to $3$. Then we solve completely the Diophantine equation $(q^n-1)/(q-1)=y$ for infinitely many values of $y$. This result finds frequent applications in the theory of finite groups.},
author = {Khosravi, Amir, Khosravi, Behrooz},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {higher order Diophantine equation; exponential Diophantine equation; exponential Diophantine equation; Fermat prime; Mersenne prime},
language = {eng},
number = {1},
pages = {1-7},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {On the Diophantine equation $\frac\{q^n-1\}\{q-1\}=y$},
url = {http://eudml.org/doc/249149},
volume = {44},
year = {2003},
}

TY - JOUR
AU - Khosravi, Amir
AU - Khosravi, Behrooz
TI - On the Diophantine equation $\frac{q^n-1}{q-1}=y$
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2003
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 44
IS - 1
SP - 1
EP - 7
AB - There exist many results about the Diophantine equation $(q^n-1)/(q-1)=y^m$, where $m\ge 2$ and $n\ge 3$. In this paper, we suppose that $m=1$, $n$ is an odd integer and $q$ a power of a prime number. Also let $y$ be an integer such that the number of prime divisors of $y-1$ is less than or equal to $3$. Then we solve completely the Diophantine equation $(q^n-1)/(q-1)=y$ for infinitely many values of $y$. This result finds frequent applications in the theory of finite groups.
LA - eng
KW - higher order Diophantine equation; exponential Diophantine equation; exponential Diophantine equation; Fermat prime; Mersenne prime
UR - http://eudml.org/doc/249149
ER -

References

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