Bugeaud, Yann ; Shorey, T. N.
(2002)
*On the Diophantine equation (x ^{m}−1)/(x−1) = (y^{n}−1)/(y−1)*
Pacific Journal of Mathematics, 207
(1).
pp. 61-75.
ISSN 0030-8730

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Official URL: http://msp.berkeley.edu/pjm/2002/207-1/p04.xhtml

## Abstract

We study the Diophantine equation x^{m}−1 x−1 = y^{n}−1 y−1 in integers x > 1, y > 1, m > 1, n > 1 with x≠y. We show that, for given x and y, this equation has at most two solutions. Further, we prove that it has finitely many solutions (x,y,m,n) with m > 2 and n > 2 such that gcd(m − 1,n − 1) > 1 and (m − 1) / (n − 1) is bounded.

Item Type: | Article |
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Source: | Copyright of this article belongs to Mathematical Sciences Publishers. |

Keywords: | Multiple Solution; Existence of Solution; Diophantine Equation; Number Theory |

ID Code: | 67728 |

Deposited On: | 31 Oct 2011 13:27 |

Last Modified: | 31 Oct 2011 13:27 |

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