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.
- Weak Convergence
- Weak Law of Large Numbers
- Weakly Binary Tree
- Weakly Complete Sequence
- Weakly Independent
- Weakly Triple-Free Set
- Weber Differential Equations
- Weber Functions
- Weber's Discontinuous Integrals
- Weber's Formula
- Weber-Sonine Formula
- Weber's Theorem
- Web Graph
- Wedderburn's Theorem
- Weddle's Rule
- Wedge
- Wedge Product
- Weekday
- Weibull Distribution
- Weierstrass M-Test
- Weierstraß Approximation Theorem
- Weierstraß-Casorati Theorem
- Weierstraß Constant
- Weierstraß Elliptic Function
- Weierstraß-Erdman Corner Condition