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

Maciej Gawron

Maciej Gawron

Colloquium Mathematicae, Tome 131 (2013), p. 53-58 / Harvested from The Polish Digital Mathematics Library

Résumé

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 $P (z) = a_{d} z^{d} + a_{d - 3} z^{d - 3} + \dots + a ₁ x + a ₀$ .

Publié le : 2013-01-01

Zbl 06184250

EUDML-ID : urn:eudml:doc:284136

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     author = {Maciej Gawron},
     title = {A note on the Diophantine equation P(z) = n! + m!},
     journal = {Colloquium Mathematicae},
     volume = {131},
     year = {2013},
     pages = {53-58},
     zbl = {06184250},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-5}
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Maciej Gawron. A note on the Diophantine equation P(z) = n! + m!. Colloquium Mathematicae, Tome 131 (2013) pp. 53-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm131-1-5/