7.4.2.1. Definition of Congruence

Try these first

1. 1.

   What is 7 mod 3?

   Hint

   Think about the division and what is left over.

2. 2.

   Is 8 congruent to 2 modulo 6?

   Hint

   Perform the division and find the remainder.

3. 3.

   What is the result of 10 mod 6?

   • 2
   • 4
   • 1

   Hint

   Divide 10 by 6 and think about what is left.

4. 4.

   True or False: If a ≡ b mod N, then a - b is divisible by N?

   • True
   • False

   Hint

   Consider the definition of what it means for two numbers to be congruent.

5. 5.

   Let a = 17 and b = 5, verify if both are congruent modulo 4 and explain your reasoning.

   Hint

   Perform the modulo operation for both a and b.

6. 6.

   If a - b = 32 and b = 12, find a and check if it is congruent with any integer c under modulus 7.

   Hint

   You first need to find a using the relationship and then find congruency with some examples.