On a conjecture of Erdos and Stewart
HTML articles powered by AMS MathViewer
- by Florian Luca PDF
- Math. Comp. 70 (2001), 893-896 Request permission
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
- Y. Bugeaud and M. Laurent, Minoration effective de la distance $p$-adique entre puissances de nombres algébriques, J. Number Theory 61 (1996), no. 2, 311–342 (French, with English summary). MR 1423057, DOI 10.1006/jnth.1996.0152
- 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.
- Richard K. Guy, Unsolved problems in number theory, 2nd ed., Problem Books in Mathematics, Springer-Verlag, New York, 1994. Unsolved Problems in Intuitive Mathematics, I. MR 1299330, DOI 10.1007/978-1-4899-3585-4
Additional Information
- Florian Luca
- Affiliation: Mathematical Institute, Czech Academy of Sciences, Z̆itná 25, 115 67 Praha 1, Czech Republic
- MR Author ID: 630217
- Email: luca@math.cas.cz
- Received by editor(s): January 4, 1999
- Published electronically: March 8, 2000
- © Copyright 2000 American Mathematical Society
- Journal: Math. Comp. 70 (2001), 893-896
- MSC (2000): Primary 11D61
- DOI: https://doi.org/10.1090/S0025-5718-00-01178-9
- MathSciNet review: 1677411