Question 85
Define a power cycle to be a set $S$ consisting of the nonnegative integer powers of an integer $a$, i.e. $S = \{1, a, a^{2}, \ldots\}$ for some integer $a$. What is the minimum number of power cycles required such that given any odd integer $n$, there exists some integer $k$ in one of the power cycles such that $n \equiv k \pmod{1024}$?