Mahler's 3/2 problem
In mathematics, Mahler's 3/2 problem concerns the existence of "-numbers".
A -number is a nonzero real number such that the fractional parts of
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
Mahler's conjecture would thus imply that exceeds. Flatto, Lagarias, and Pollington showed that
for rational in lowest terms.