7.3. Introduction to Number Theory

Try these first

1. 1.

   What is 10 modulo 3?

   Hint

   Divide 10 by 3 and find the remainder.

2. 2.

   Are 14 and 10 congruent modulo 4?

   Hint

   Calculate the remainder for both when divided by 4.

3. 3.

   What is 9 modulo 4?

   • 1
   • 2
   • 3
   • 0

   Hint

   Think about how many times 4 goes into 9.

4. 4.

   True or False: Division in modular arithmetic is straightforward.

   • True
   • False

   Hint

   Recall the difficulties surrounding modular inverses.

5. 5.

   Calculate (29 + 13) mod 10 and explain each step involved.

   Hint

   Think of it as simplifying operations with the modulus before finding the result.

6. 6.

   Using the square and multiply method, compute 3^20 mod 5. Show your workings.

   Hint

   Focus on the binary representation of 20 to simplify multiplications.