7.2. Lecture - 55: Modular Arithmetic

Try these first

1. 1.

   What is 7 mod 3?

   Hint

   Think about how many times 3 can fit into 7.

2. 2.

   Explain what it means for two numbers to be congruent modulo N.

   Hint

   Consider the definition of congruence.

3. 3.

   What is the result of 10 mod 3?

   • 1
   • 2
   • 3

   Hint

   Sit down and think about how many times 3 goes into 10.

4. 4.

   Is the statement '6 ≡ 2 (mod 4)' true?

   • True
   • False

   Hint

   Calculate 6 mod 4 and see if it equals 2.

5. 5.

   Prove that if a ≡ b (mod N) and c is an integer, then a + c ≡ b + c (mod N).

   Hint

   Rewrite a in terms of its congruence definition.

6. 6.

   Find all integers x such that 2x ≡ 1 (mod 3).

   Hint

   Try small integers and check their congruence.