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On a conjecture of Erdos and Stewart

Author: Florian Luca
Journal: Math. Comp. 70 (2001), 893-896
MSC (2000): Primary 11D61
Published electronically: March 8, 2000
MathSciNet review: 1677411
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Abstract: For any $k\ge 1$, let $p_k$ be the $k$th prime number. In this paper, we confirm a conjecture of Erdős and Stewart concerning all the solutions of the diophantine equation $n!+1=p^a_kp^b_{k+1}$, when $p_{k-1}\le n<p_k$.

References [Enhancements On Off] (What's this?)

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  • P. Erdős & R. Obláth, Über diophantische Gleichungen der Form $n!=x^p\pm y^p$ und $n!\pm m!=x^p$, Acta Szeged 8 (1937), 241–255.
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Additional Information

Florian Luca
Affiliation: Mathematical Institute, Czech Academy of Sciences, Z̆itná 25, 115 67 Praha 1, Czech Republic
MR Author ID: 630217

Keywords: $p$-adic linear forms in two logarithms
Received by editor(s): January 4, 1999
Published electronically: March 8, 2000
Article copyright: © Copyright 2000 American Mathematical Society