7.4.3.1. Addition and Subtraction Rules

Try these first

1. 1.

   Calculate 12 mod 5.

   Hint

   Think about how many times `5` fits into `12`.

2. 2.

   What is 9 mod 4?

   Hint

   Consider the remainder when you divide `9` by `4`.

3. 3.

   If 8 ≡ x (mod 5) and x = 3, what is true?

   • True
   • False

   Hint

   Consider how both numbers interact with `5`.

4. 4.

   In modular arithmetic, a + b (mod N) is equivalent to:

   • a + b
   • a mod N + b mod N
   • a + b + N

   Hint

   Revisit how remainders are calculated.

5. 5.

   Explore the implications of 15 ac ≡ 5 bc (mod 10). Under what conditions can 'c' be cancelled from both sides?

   Hint

   Consider when numbers become zero mod 10.

6. 6.

   Demonstrate the failure of division in modular arithmetic by finding values of a and b such that a/b (mod 8) yields an invalid conclusion.

   Hint

   Explore values that don’t yield clean divisions.