Quiz8
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School
City College of San Francisco *
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Course
115
Subject
Mathematics
Date
Feb 20, 2024
Type
Pages
4
Uploaded by ConstableJellyfishMaster2657
Question 1 0/1pts a=bmodn < n|(b-a) True VFalse Question 2 1/1pts Two numbers are congruent modulo 10 if and only if they have the same last digit. True False Question 3 1/1pts a=bmodn < rem(a,n) = rem(b, n) True False Question 4 1/1pts What is 287° congruent to modulo 47 Enter a result that is in the interval [0. . 4). Question 5 1/1pts Suppose that both of the following are true: =bmod n d mod n Which of the following must be true as a result of this assumption? Choose all that apply.
Question 6 1/1pts Ifa-c=b-cmodn, thena=bmodn. True False Question 7 1/1pts Suppose that ged(k, n) = 1. Avalue k' is an inverse of k modulo n whenever k' - k is congruent to what number (modulo ) ? 1 Question 8 1/1pts Wfa-k=b-kmodn andged(k.m) = 1, thena = bmod . True False Question 9 1/1pts Choose all the following that are equivalent statements. kis cancellable modulo n k has an inverse modulo n kis relatively prime to n Question 10 1/1pts How integers in the intervale [0.. 31) are relative prime to 317 (Note that 31 is a prime number).
Question 11 1/1pts If k is relatively prime to 1, then k%" is congruent to what value (modulo n)? Question 12 1/1pts What s the value of 3+ 6 in the ring Z7? Question 13 1/1pts jmodn < rem(i, n) = rem(j. n) (Z,) True False Question 14 1/1pts Ifi € Zj,, then i is relatively prime to n. True False Question 15 1/1pts ‘What is the remainder formed from dividing (444273456™9 4 15555858557 . 4030666666y 367 27
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Question 16 1/1pts 3 has a multiplicative inverse in Z 5 True False Question 17 1/1pts ¢(pg) = (p—1)(g—1) forprimesp # q. True False Question 18 1/1pts What is the value of ¢p(12)? Question 19 1/1pts If e is a relatively prime to ¢p(n) = (p — 1)(g — 1), then there exists d € [0..¢p(n)) suchthate -d = 1 mod ¢p(n) . True False