n this problem, we will carry out some steps of the quantum factoring algorithm for N=15.

Question

(a) What is the period k of the periodic superposition set up by the quantum factoring algorithm if it chooses x=2?
(b) Assume that we found this k using period finding algorithm. Use k to find a non-trivial square root of 1(mod15). Write your answer as an integer between 0 and 15.
(c) Then, the algorithm proceeds by computing gcd(x,y) for some integers x and y. List these two numbers separated by a comma.

If there are more than one correct solution, provide any one of them.