In mathematics, Mahler's 3/2 problem concerns the existence of "-numbers".
A -number is a real number such that the fractional parts of
x\left(
| 3 | |
| 2\right) |
n
are less than for all positive integers . Kurt Mahler conjectured in 1968 that there are no -numbers.
More generally, for a real number, define as
\Omega(\alpha)=inf\theta>0\left({\limsupn\left\lbrace{\theta\alphan}\right\rbrace-\liminfn\left\lbrace{\theta\alphan}\right\rbrace}\right).
Mahler's conjecture would thus imply that exceeds . Flatto, Lagarias, and Pollington showed[1] that
| \Omega\left( | p |
| q\right) |
>
| 1 | |
| p |
for rational in lowest terms.