I have three numbers x, a, and c, where both a and c are odd numbers. The number x is the output of the following function:
$$ x = a^b\!\!\!\!\!\!\!\mod{c} $$
I am attempting to determine whether the input exponent, b, was an odd or even number based on the knowledge of the three values, a, c, and x. Is there a way to deduce the parity of the exponent b using this information?
