7.4.2. Congruence with Respect to Modulo

Try these first

1. 1.

   What is 9 mod 4?

   Hint

   Divide 9 by 4 and find the remainder.

2. 2.

   Is 7 ≡ 2 (mod 5)?

   Hint

   Check the difference of the numbers.

3. 3.

   What is 11 mod 4?

   • 2
   • 3
   • 1

   Hint

   Perform integer division and focus on the leftover.

4. 4.

   Is it possible to cancel numbers in a modular division?

   • True
   • False

   Hint

   Remember examples that contradict this.

5. 5.

   Find all integers A where A ≡ 3 (mod 5) and A ≤ 20.

   Hint

   List multiples of 5 and add 3.

6. 6.

   Explain how to prove that two numbers are congruent if their difference is divisible by the modulus.

   Hint

   Focus on expressing remainders.