A note on the Diophantine equation P(z) = n! + m!

Maciej Gawron. "A note on the Diophantine equation P(z) = n! + m!." Colloquium Mathematicae 131.1 (2013): 53-58. <http://eudml.org/doc/284136>.

@article{MaciejGawron2013,
abstract = {We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d ≥ 2 and $P(z) = a_dz^\{d\} + a_\{d-3\}z^\{d-3\} + ⋯ + a₁x + a₀$.},
author = {Maciej Gawron},
journal = {Colloquium Mathematicae},
keywords = {brocard-Ramanujan type equation; ABC conjecture; Diophantine equation},
language = {eng},
number = {1},
pages = {53-58},
title = {A note on the Diophantine equation P(z) = n! + m!},
url = {http://eudml.org/doc/284136},
volume = {131},
year = {2013},
}

TY - JOUR
AU - Maciej Gawron
TI - A note on the Diophantine equation P(z) = n! + m!
JO - Colloquium Mathematicae
PY - 2013
VL - 131
IS - 1
SP - 53
EP - 58
AB - We consider the Brocard-Ramanujan type Diophantine equation P(z) = n! + m!, where P is a polynomial with rational coefficients. We show that the ABC Conjecture implies that this equation has only finitely many integer solutions when d ≥ 2 and $P(z) = a_dz^{d} + a_{d-3}z^{d-3} + ⋯ + a₁x + a₀$.
LA - eng
KW - brocard-Ramanujan type equation; ABC conjecture; Diophantine equation
UR - http://eudml.org/doc/284136
ER -