Glasnik Matematicki, Vol. 48, No. 1 (2013), 31-48.

ON THE DIOPHANTINE EQUATION F(N)=U!+V!

Florian Luca

Fundación Marcos Moshinsky, Universidad Nacional Autonoma de México, Circuito Exterior, C.U., Apdo. Postal 70-543, Mexico D.F. 04510, Mexico
e-mail: fluca@matmor.unam.mx


Abstract.   In this paper, we show under the abc conjecture that the Diophantine equation f(x)=u!+v! has only finitely many integer solutions (x,u,v) whenever f(X) Q[X] is a polynomial of degree at least three.

2010 Mathematics Subject Classification.   11D85.

Key words and phrases.   Factorials, polynomials, applications of the abc conjecture.


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DOI: 10.3336/gm.48.1.03


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