7.4.2.2. Arithmetic Rules in Modular Arithmetic

Try these first

1. 1.

   What is 15 mod 4?

   Hint

   Subtract multiples of 4 from 15.

2. 2.

   Is 8 ≡ 2 mod 6 true or false?

   Hint

   Check the difference between 8 and 2.

3. 3.

   What is the result of 12 mod 5?

   • 1
   • 2
   • 3
   • 4

   Hint

   Perform the division and find the leftover.

4. 4.

   6 ≡ 0 mod 3 is true or false?

   • True
   • False

   Hint

   Consider the definition of congruence.

5. 5.

   If a = 17, b = -5, and N = 6, find a * b mod N.

   Hint

   Calculate the product first, then reduce using mod.

6. 6.

   Demonstrate, with a counterexample, that you cannot cancel terms in modular division.

   Hint

   Find values where the terms are not congruent.