Discrete Math

(12) Solve the linear congruence 17x E 11 (mod 75) using the following steps: a. [3] Execute the Euclidean Algorithm on 17 and 75 to show that these integers are relatively prime. This implies that a solution exists. b. [3) Reverse the steps in part a above to determine the multiplicative inverse of 17 mod 75. The steps you follow might lead you to a negative integer. Add 75 to this quantity so that your inverse is positive. c. [3] Multiply both sides of the congruence by the multiplicative inverse that you found in part b. Reduce the right-hand-side mod 75 [that is, divide by 75 and keep the remainder]. This number is your solution. (1. [3] Finally substitute your solution back into the original congruence and conrm that your solution is correct