A note on the Diophantine equation $P(z)=n!+m!$
Volume 131 / 2013
Colloquium Mathematicum 131 (2013), 53-58
MSC: Primary 11D85.
DOI: 10.4064/cm131-1-5
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 $d\geq 2$ and $P(z)=a_dz^d+a_{d-3}z^{d-3}+\cdots +a_1x+a_0$.
