Modular Arithmetic

Question 1

What is a^p - a always equal to (where p is prime and a is any natural number)?

Answer 1

An integer multiple of p

Question 2

What does a^p always equal in modular arithmetic?

Answer 2

a mod p

Question 3

What does a^(p-1) always equal in modular arithmetic?

Answer 3

1 mod p

Question 4

What is 2+7 in modulo 12?

Answer 4

9 mod 12

Question 5

What is 6+10 in modulo 12?

Answer 5

4 mod 12

Question 6

What is 4+8 in modulo 12?

Answer 6

0 mod 12

Question 7

What are the next five numbers that 1 is also equal to in modulo 12?

Answer 7

13, 25, 37, 49, 61

Question 8

What are the next five numbers that 10 is equal to in modulo 12?

Answer 8

22, 34, 46, 58, 70

Question 9

If a = b mod 12 then what does a-b =?

Answer 9

a-b = a multiple of 12

Question 10

If 56=20 mod 12 then what is (56-20)%12?

Answer 10

0

Question 11

In mod 5, what can every integer be expressed as?

Answer 11

0, 1, 2, 3, 4

Question 12

What is the residue class of [4]’5

Answer 12

{…-16,-11,-6,-1, 4, 9, 14, 19…}

Question 13

How do you know if b is a primitive root of p?

Answer 13

B^1, B^2… B^(P-1) = An arrangement of 1, 2 … P-1