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A note on the Diophantine equation P(z) = n! + m!

Maciej Gawron (2013)

Colloquium Mathematicae

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 ≥ 2 and P ( z ) = a d z d + a d - 3 z d - 3 + + a x + a .

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