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

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

Florian Luca

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.