# On the diophantine equation xp - x = yq - y.

Maurice Mignotte; Attila Petho

Publicacions Matemàtiques (1999)

- Volume: 43, Issue: 1, page 207-216
- ISSN: 0214-1493

## Access Full Article

top## Abstract

top## How to cite

topMignotte, Maurice, and Petho, Attila. "On the diophantine equation xp - x = yq - y.." Publicacions Matemàtiques 43.1 (1999): 207-216. <http://eudml.org/doc/41357>.

@article{Mignotte1999,

abstract = {We consider the diophantine equation(*) xp - x = yq - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.},

author = {Mignotte, Maurice, Petho, Attila},

journal = {Publicacions Matemàtiques},

keywords = {Ecuaciones diofánticas; Números enteros; exponential diophantine equations; -integers; integral solutions; rational solutions; finiteness theorem; -conjecture; rational points},

language = {eng},

number = {1},

pages = {207-216},

title = {On the diophantine equation xp - x = yq - y.},

url = {http://eudml.org/doc/41357},

volume = {43},

year = {1999},

}

TY - JOUR

AU - Mignotte, Maurice

AU - Petho, Attila

TI - On the diophantine equation xp - x = yq - y.

JO - Publicacions Matemàtiques

PY - 1999

VL - 43

IS - 1

SP - 207

EP - 216

AB - We consider the diophantine equation(*) xp - x = yq - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.

LA - eng

KW - Ecuaciones diofánticas; Números enteros; exponential diophantine equations; -integers; integral solutions; rational solutions; finiteness theorem; -conjecture; rational points

UR - http://eudml.org/doc/41357

ER -