1-Jan-1995
Unsolved Problem 1:
Are 8 and 9 the only consecutive powers?
An integer is a perfect power if it is of the form
m^n where m and n are integers and n>1.
It is conjectured that 8=2^3 and 9=3^2 are
the only consecutive integers that are perfect powers.
Reference:
- [Ribenboim 1994]
- Paulo Ribenboim,
Catalan's Conjecture.
Academic Press. Boston: 1994.
Catalan's Conjecture
Each week, for your edification, we publish a well-known
unsolved mathematics problem. These postings are intended
to inform you of some of the difficult, yet
interesting, problems that mathematicians
are investigating. We do not suggest that you tackle these problems,
since mathematicians have been unsuccessfully working on these
problems for many years.
general references
problem archive
next problem
electronic publications