Modulular Arithmetic

What is 244 mod 7?

• 6
• 5
• 3
• 1

What is 347 mod 5?

• 1

• 2

• 3

• 4

What is 150 mod 8?

• 6

• 0

• 4

• 2

Which of the following numbers is congruent to 5 modulo 9?

• 50

• 41

• 32

• 23

What is the remainder when 563 is divided by 11?

• 3

• 2

• 4

• 1

Which of the following does not belong to the same class as the others modulo 6?

• 602

• 122

• 86

• 72

If a ≡ 12 mod 16, and b ≡ 10 mod 16, and (a + b) mod 16 ≡ x mod 16, then what is x?

• 0

• 6

• 8

• 14

In modulo 11, what is the multiplicative inverse of 8?

• 2

• 4

• 7

• 9

For which example does a multiplicative inverse not exist?

• 5 mod 7

• 7 mod 10

• 10 mod 20

• 20 mod 41

Answer explanation

The multiplicative inverse when multiplied with the original number will return a modulus of 1 (therefore their product is one greater than some multiple of the divisor).

When the input is a factor of the divisor (i.e. 10 is a factor of 20), it is impossible to find a number to satisfy this. 10 multiplied by any number will only return a modulus of itself or 0.

A Caesar cypher has an encryption key of "a → D". What is the encrypted text for "Dog"?

• ALD

• HSK

• GRJ

• FQI