#### Glasnik Matematicki, Vol. 37, No.2 (2002), 269-273.

### THE DIOPHANTINE EQUATION
*P*(*x*) = *n*! AND A RESULT OF M. OVERHOLT

### Florian Luca

Mathematical Institute, UNAM, Ap. Postal 61-3 (Xangari),
CP 58089, Morelia, Michoacan, Mexico

*e-mail:* `fluca@matmor.unam.mx`

**Abstract.** In this note, we show that the ABC-conjecture
implies that a diophantine equation of the form
*P*(*x*) = *n*! with *P* a
polynomial with integer coefficients and degree
*d* > 1 has only
finitely many integer solutions (*x*,*n*) with
*n* > 0.

**2000 Mathematics Subject Classification.**
11D85.

**Key words and phrases.** ABC-Conjecture, diophantine
equations.

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