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On a conjecture of Erdos and Stewart

Author(s): Florian Luca.
Journal: Math. Comp. 70 (2001), 893-896.
MSC (2000): Primary 11D61
Posted: March 8, 2000
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Abstract:

For any $k\ge1$ , let be the th prime number. In this paper, we confirm a conjecture of Erdos 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:

[1]: Y. Bugeaud & M. Laurent, Minoration effective de la distance -adique entre puissances de nombres algébriques, J. Number Theory 61 (1996), 311-342. MR 98b:11086
[2]: P. Erdos & 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.
[3]: R. K. Guy, Unsolved problems in number theory, Springer-Verlag, New York, 1994, Problem A2.MR 96e:11002


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