Now suppose a is any integer relatively prime to p. We take successive powers of a modulo p until we find an instance where a' = qu . . . qi, where e1, .... ex E N. Find and prove a congruence for ind, (a) that uses this information and the data produced by the procedure in question 1b.2. The method for computing ind, (a) you found in question 1 is called the inder calculus. In this question we use it to compute an example. a. Use the method discussed in class to show that 2 is a primitive root modulo 83. b. Let q1 = 2, 92 = 3, 93 = 5, and q4 = 7. Take successive powers of 2 modulo 83 until you have found a sufficient number of congruences of the form discussed in question 1b. Use these congruences to find ind2(2). ind2(3), ind2(5), and ind2(7). c. Use the method outlined in question Ic to find ind2(31)