A note on the diophantine equation ${k\atopwithdelims ()2}-1=q^n+1$

Le, Maohua

A note on the diophantine equation

(\binom{k}{2}) - 1 = q^{n} + 1

Le, Maohua

Colloquium Mathematicae, Tome 78 (1998), p. 31-34 / Harvested from The Polish Digital Mathematics Library

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Résumé

In this note we prove that the equation $(\binom{k}{2}) - 1 = q^{n} + 1$ , $q \geq 2, n \geq 3$ , has only finitely many positive integer solutions $(k, q, n)$ . Moreover, all solutions $(k, q, n)$ satisfy $k 10^{10^{182}}$ , $q 10^{10^{165}}$ and $n 2 \cdot 10^{17}$ .

Publié le : 1998-01-01

Zbl 0909.11012

EUDML-ID : urn:eudml:doc:210550

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     author = {Maohua Le},
     title = {A note on the diophantine equation ${k\atopwithdelims ()2}-1=q^n+1$
            },
     journal = {Colloquium Mathematicae},
     volume = {78},
     year = {1998},
     pages = {31-34},
     zbl = {0909.11012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-cmv76z1p31bwm}
}

Le, Maohua. A note on the diophantine equation ${k\atopwithdelims ()2}-1=q^n+1$
            . Colloquium Mathematicae, Tome 78 (1998) pp. 31-34. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-cmv76z1p31bwm/

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