In this problem, we will carry out some steps of the quantum factoring algorithm for N=91.

Question

(a) What is the period k of the periodic superposition set up by the quantum factoring algorithm if it chooses x=8? I.e. what is the period of f(j)=8j(mod91)
(b) Using your answer to (a), find a nontrivial square root of 1(mod91). Write your answer as an integer between 0 and 91.
(c) Then, the algorithm proceeds by computing gcd(91,y) for some y. What is y? If there are multiple correct answers, provide any one of them.

Answer 1

6.(a)answer: 4