In mathematics, Mahler's 3/2 problem concerns the existence of "-numbers".
A -number is a positive 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 follow if exceeds . Flatto, Lagarias, and Pollington showed that
for rational in lowest terms.
References