Aperiodic Binary Strings Redux

A binary string is a string whose characters are only 0s and/or 1s. For example, \(0101, 11111, 110001\) are binary strings.

A string \(s\) is periodic if there exists another string \(t\) whose length is less than \(s\) such that concatenating several copies of \(t\) produces \(s\). For example, \(0101\) is periodic (\(t = 01\)), and \(1111\) is periodic (\(t = 11\) or \(t = 1\)), but \(10101\) is not periodic. A string is aperiodic if it is not periodic.

This problem asks about the number of aperiodic binary strings of length \(23\). For this problem, compute the number of aperiodic binary strings of length \((23!)^{23}\) (that is, 23 factorial raised to the 23th power). Enter your answer modulo \(10^9 + 7 = 1000000007\).


Clearly inspired from the linked problem above.
×

Problem Loading...

Note Loading...

Set Loading...