Question 67
Does there exist an irrational number $\alpha\gt 1$ such that
$$
\left\lfloor\alpha^{n}\right\rfloor \equiv 0 \quad(\bmod 2017)
$$
for all integers $n \geq 1$?
$$
\left\lfloor\alpha^{n}\right\rfloor \equiv 0 \quad(\bmod 2017)
$$
for all integers $n \geq 1$?