We show the existence of ``good'' approximations to a real number $\gamma$ using rationals with denominators formed by digits $0$ and $1$ in base $b$. We derive an elementary estimate and enhance this result by managing exponential sums.
Beta-expansion and continued fraction expansion of real numbers
On uniform approximation to successive powers of a real number
Addendum to: On the rational approximation of the sum of the reciprocals of the Fermat numbers
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