MATH236 Test 3 Thu May 19 2022Page 1 of 6 The duration of the test is 90 minutes. There are 21 questions. Total mark: 100. Scan only the answer table and your answer to the written questions 17–21. Select exactlyoneof the given choices A, B, C, D, E in each of Questions 1–16 and enter your choices into the table below. Question12345678910111213141516 Answer 1. (3 points) Consider the following sequences of statements. (1)Leta,b∈NandX={ax+by:x,y∈Z}. (2)Sincex=1andy=0are integers,Xhas a positive member. (3)Letd∈Xbe the smallest positive element ofX. (4)ThenX={kd:k∈Z}. (5)a=k1dandb=k2 d. (6)By (5),d|aandd|b. (7)Henced=(a,b). A. (3) is true by the definition ofXand(B)is true sinceXis closed under addition and division. B. (3) is true by the Archimedean principle, (4) is is true sinceXis closed under addition and subtraction, and (7) is true since for everyc,c|aandc|bimplies thatd|c. C. (3) and (5) are true by the Archimedean principle. D. (3), (5), (7) are false and (4) is true. E. (3), (4), (5), (7) are false.
2. (3 points) Let(n,e)and(n,d)be the encryption and decryption keys of an RSA cryptosys- tem. Then
