Catalan's Diophantine Problem
Find consecutive Powers, i.e., solutions to
excluding 0 and 1. Catalan's Conjecture is that the only solution is
, so 8 and 9 (
and 
)are the only consecutive Powers (again excluding 0 and 1).See also Catalan's Conjecture
References
Cassels, J. W. S. ``On the Equation Inkeri, K. ``On Catalan's Problem.'' Acta Arith. 9, 285-290, 1964.
. II.'' Proc. Cambridge Phil. Soc. 56, 97-103, 1960.
- Burnside's Lemma
- Busemann-Petty Problem
- Busy Beaver
- Small Multiple Method
- Small Number
- Small Retrosnub Icosicosidodecahedron
- Small Rhombicosidodecahedron
- Small Rhombicuboctahedron
- Small Rhombidodecacron
- Small Rhombidodecahedron
- Small Rhombihexacron
- Small Rhombihexahedron
- Small Snub Icosicosidodecahedron
- Small Stellapentakis Dodecahedron
- Small Stellated Dodecahedron
- Small Stellated Triacontahedron
- Small Stellated Truncated Dodecahedron
- Small Triakis Octahedron
- Small Triambic Icosahedron
- Small World Problem
- Smarandache Ceil Function
- Smarandache Constants
- Smarandache Function
- Smarandache-Kurepa Function
- Smarandache Near-to-Primorial Function