Glasnik Matematicki, Vol. 37, No.2 (2002), 269-273.
THE DIOPHANTINE EQUATION
P(x) = n! AND A RESULT OF M. OVERHOLT
Mathematical Institute, UNAM, Ap. Postal 61-3 (Xangari),
CP 58089, Morelia, Michoacan, Mexico
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.
Key words and phrases. ABC-Conjecture, diophantine
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