Geodesic
A note on the Diophantine equation $P(z)=n!+m!$
Maciej Gawron1
1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland
Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 53-58 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $P(z)=a_dz^d+a_{d-3}z^{d-3}+\cdots +a_1x+a_0$.
DOI : 10.4064/cm131-1-5
Mots-clés : consider brocard ramanujan type diophantine equation where polynomial rational coefficients abc conjecture implies equation has only finitely many integer solutions geq d d cdots

Maciej Gawron 1

1 Institute of Mathematics Jagiellonian University Łojasiewicza 6 30-348 Kraków, Poland 
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Maciej Gawron. A note on the Diophantine equation $P(z)=n!+m!$. Colloquium Mathematicum, Tome 131 (2013) no. 1, pp. 53-58. doi: 10.4064/cm131-1-5

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