Modular Arithmetic

Question 1

If x=
7 mod 4, then x can be?

a. 2
b. 1
c. 3

Answer 1

3

Question 2

If 12 mod 5 = x , then x can be
a. 2
b. 3
c. 5

Answer 2

2

Question 3

What is 100 mod 11?

a. 1
b. 0
c. 2

Answer 3

1

Question 4

Which of the following solves 2 x = 5 mod 3?

a. 5

b. 10

c. 6

Answer 4

10

Question 5

If x + 3 = -1 mod 5, then x can be

a. 1

b. - 3

c. 2

Answer 5

1

Question 6

congruent or not

30 = 11 ( mod 3)

Answer 6

not

Question 7

congruent or not

-6 = 5 ( mod 2)

Answer 7

not

Question 7

congruent or not

18 = -7 (mod 5)

Answer 7

congruent

Question 8

congruent or not

12 = 24 ( mod 6)

Answer 8

congruent

Question 9

congruent or not

13 = 13 ( mod 7)

Answer 9

congruent

Question 10

congruent or not

-10 = -32 (mod 4)

Answer 10

not

Question 11

In cryptography, encryption is the process of transforming the original representation of an information, known as ______ into an alternative (or secret) form known as _______

Answer 11

plaintext, cyphertext

Question 12

caesar cypher decoding formula

Answer 12

y = 3x + 2(mod 26)

Question 13

decode the letter T = 20 using the caesar cypher

Answer 13

= 3(20) + 2 (mod 26)
= 62 (mod 26)
= 10 (mod 26)

Question 14

formul for caesar cypher inverse

Answer 14

y≡9(x−2) (mod26)

Question 15

solve for addition modulo m

8⊕7 ≡ 15 (mod9)

Answer 15

= 6 (mod 9)

Question 16

solve for multiplication modulo m
8⊗7 ≡ 56 (mod9)

Answer 16

≡ 2 (mod 9).

Question 17

when the modulus m = 4, we have

Answer 17

Z4 = {0,1,2,3}.