In mathematics, Mahler's 3/2 problem concerns the existence of "Z-numbers".
A Z-number is a real number x such that the fractional parts of
are less than 1/2 for all positive integers n. Kurt Mahler conjectured in 1968 that there are no Z-numbers.
More generally, for a real number α, define Ω(α) as
Mahler's conjecture would thus imply that Ω(3/2) exceeds 1/2. Flatto, Lagarias, and Pollington showed[1] that
for rational p/q > 1 in lowest terms.