Modular Arithmetic

Question 1

the range of a mod n

Answer 1

0 to n-1

Question 2

5 mod 11

Answer 2

5

Question 3

17 mod 11

Answer 3

6

Question 4

11 mod 11

Answer 4

0

Question 5

-12 mod 11

Answer 5

10

Question 6

≈ denotes ___ in modulo arithmetic

Answer 6

congruence

Question 7

refers to numbers that have the same modular value

Answer 7

congruence

Question 8

Note that congruent numbers differ by multiples of…

Answer 8

the modulus

Question 9

For large values, we can use ___ to simplify modular computations.

Answer 9

modulo reduction

Question 10

( ( a mod n ) + ( b mod n ) ) mod n =

Answer 10

( a + b ) mod n

Question 11

( 12 + 8 ) mod 5 =

Answer 11

( 12 + 8 ) mod 5 = ( ( 12 mod 5 ) + ( 8 mod 5 ) ) mod 5 = ( 2 + 3 ) mod 5 = 5 mod 5 = 0

Question 12

( 12 * 8 ) mod 5 =

Answer 12

( 12 * 8 ) mod 5 = ( ( 12 mod 5 ) * ( 8 mod 5 ) ) mod 5 = ( 2 * 3 ) mod 5 = 6 mod 5 = 1

Question 13

2^6 mod 5 =

Answer 13

2^6 mod 5 = ( ( 2^2 mod 5 ) * ( 2^4 mod 5 ) ) mod 5 = ( 4 mod 5 ) * ( 16 mod 5 ) = (4*1) mod 5 = 4

Question 14

3^7 mod 5 =

Answer 14

2

Question 15

if x and y are mod inverses, x and y must be…

Answer 15

less than the modulus

Question 16

Not all values less than a particular modulus have…

Answer 16

inverses

Question 17

the inverse of 7 mod 10

Answer 17

3

Question 18

x and y are mod inverses mod n if x and y are less than n and…

Answer 18

x*y mod n = 1