7.4.1. Definition and Concept of Modulus

Try these first

1. 1.

   What is 8 mod 3?

   Hint

   Consider how many times 3 goes into 8.

2. 2.

   Calculate -10 mod 5.

   Hint

   Think about watching -10 on the number line.

3. 3.

   What is the result of 14 mod 5?

   • 2
   • 4
   • 3

   Hint

   How many times does 5 go into 14, and what is left over?

4. 4.

   True or False: -1 mod 5 equals 4.

   • True
   • False

   Hint

   Think about adjusting -1 to the range of positive numbers.

5. 5.

   Prove that if a ≡ b mod N, then b ≡ a mod N.

   Hint

   Consider rearranging the congruence definition.

6. 6.

   If you have 7 along with 17, what can you conclude about their congruence under a modulus of 5?

   Hint

   Calculate each one's modulus first.