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

Mignotte, 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 &lt; 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 &lt; 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 -