  I solve here a question of Vladimir Reshetnikov in Mathoverflow (question
261649) about the values of Fabius function. Namely, I prove that the numbers
$R_n:=2^{-\binom{n-1}{2}}(2n)! F(2^{-n})\prod_{m=1}^{\lfloor
n/2\rfloor}(2^{2m}-1)$ are integers. We show also some other arithmetical
properties of the values of Fabius function at dyadic points. The Fabius
function was defined in 1935 by Jessen and Wintner and has been independently
defined at least six times since. We attempt to unify notations related to the
Fabius function.
