A+ CATEGORY SCIENTIFIC UNIT

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

Volume 131 / 2013

Maciej Gawron Colloquium Mathematicum 131 (2013), 53-58 MSC: Primary 11D85. DOI: 10.4064/cm131-1-5

Abstract

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 $d\geq 2$ and $P(z)=a_dz^d+a_{d-3}z^{d-3}+\cdots +a_1x+a_0$.

Authors

  • Maciej GawronInstitute of Mathematics
    Jagiellonian University
    Łojasiewicza 6
    30-348 Kraków, Poland
    e-mail

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