7.4.3. Arithmetic Rules of Modular Arithmetic

Try these first

1. 1.

   What is 18 mod 5?

   Hint

   Find how many times 5 fits into 18, and what’s left over.

2. 2.

   Calculate (4 + 6) mod 5.

   Hint

   Add the numbers first, then find the remainder when divided by 5.

3. 3.

   What is 9 mod 4?

   • 1
   • 2
   • 3

   Hint

   Perform the division and find the leftover.

4. 4.

   Is division always defined in modular arithmetic?

   • True
   • False

   Hint

   Think about how division handles negative or smaller numbers in the modulus.

5. 5.

   Using the square-and-multiply algorithm, find 7^23 mod 5.

   Hint

   Convert the exponent to binary first.

6. 6.

   Provide a real-world application of modular arithmetic in cryptography.

   Hint

   Think about how encrypting messages requires specific math operations that secure them.