Fermat's Little Theorem says that if a, pZ with p prime and a not divisible by p then a-1=1 mod p. In the question below, it will be helpful for you to remember the notion of order of an element a E Fo and how it is an integer (dividing 10091) depending on a. 1009, (a) Assuming Fermat's Little Theorem, and assuming xEZ, please find a simple character- ization for when 11 = 114 mod 1009. Hint: Could it be a congruence involving x? If so, what would the modulus be? (b) Please find a simple characterization for when 121 1214 mod 1009. (c) If you consider x {0,..., 1007} which happens more often: 11 = 114 mod 1009 or