Fermat's Theorem

Fermat's little theorem states that if a

a and p are coprime positive integers, with

p prime, then a^p-1 (mod p) = 1

Which of the following congruences satisfies the conditions of this theorem?

• 12⁶ mod 7=1

• 14⁷ mod 8=1

• 16⁸ mod 9 = 1

• 18⁹ mod 10=1

What is the remainder when 3⁴⁵⁶ is divided by 7?

• 1

• 2

• 3

• 4

True or false?

42⁶ mod 7=1.

• True

• False

32²³ (mod 23)=?

• 5

• 7

• 9

• 11

1⁴ mod 5 = 1

2⁴ mod 5 = 1

3⁴ mod 5 = 1

4⁴ mod 5 = 1​

​

We are given that the 4 congruences above are true. Is the following congruence true as well?

5⁴ mod 5=1

• Yes, it is true

• No , it is not true