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

• Autorzy: Maciej Gawron
• Języki publikacji: EN

Abstrakty

EN

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 $P(z) = a_dz^{d} + a_{d-3}z^{d-3} + ⋯ + a₁x + a₀$.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2013
• Tom: 131
• Numer: 1
• Strony: 53-58

Daty

wydano

2013

Twórcy

autor

Maciej Gawron

• Institute of Mathematics, Jagiellonian University, Łojasiewicza 6, 30-348 Kraków, Poland

Identyfikatory

DOI

10.4064/cm131-1-5