7.4.3.3. Division in Modular Arithmetic

Try these first

1. 1.

   Calculate 10 mod 3.

   Hint

   Think about dividing 10 by 3 and looking for the remainder.

2. 2.

   What is -7 mod 5?

   Hint

   Adjust -7 into the positive range before calculating the mod.

3. 3.

   What does 'a ≡ b (mod N)' mean?

   • a is greater than b
   • a and b give the same remainder when divided by N
   • a is divisible by N

   Hint

   Think about the remainder from the division.

4. 4.

   True or False: Division in modular arithmetic can always be performed.

   • True
   • False

   Hint

   Reflect on what happens when you divide numbers.

5. 5.

   Given a = 17, b = 5, and N = 6, perform the operation a - b and then find the modulo.

   Hint

   First perform the subtraction, then apply modulo.

6. 6.

   Can you determine the conditions under which modular division is valid if a = 15, b = 5, and N = 8?

   Hint

   Check if the divisor b is invertible mod N.