Fermat's Little Theorem and Modular Arithmetic

The video tutorial introduces Fermat's Little Theorem and demonstrates its application in finding the least residue of large numbers when divided by a prime number. Three examples are provided: a small number for calculator verification, a larger number that exceeds typical calculator capacity, and a very large number with over 300 digits. The tutorial explains how to use the theorem to simplify calculations and find remainders efficiently.

What is Fermat's Little Theorem primarily used for?

• Finding the least residue of a number when divided by a prime

• Calculating the square root of a number

• Determining the greatest common divisor

• Solving linear equations

In Fermat's Little Theorem, if 'a' is an integer and 'p' is a prime, what is the expression for the theorem?

• a^(p-1) ≡ 1 (mod p)

• a^(p+1) ≡ 1 (mod p)

• a^(p-1) ≡ 0 (mod p)

• a^(p+1) ≡ 0 (mod p)

What is the significance of the number 1 in Fermat's Little Theorem?

• It represents the base of the power

• It is the remainder when a^(p-1) is divided by p

• It is the prime number used in the theorem

• It is the exponent in the theorem

What is the significance of the number 1 in Fermat's Little Theorem?

• It represents the base of the power

• It is the remainder when a^(p-1) is divided by p

• It is the prime number used in the theorem

• It is the exponent in the theorem

What is the significance of the number 1 in Fermat's Little Theorem?

• It represents the base of the power

• It is the exponent in the theorem

• It is the remainder when a^(p-1) is divided by p

• It is the prime number used in the theorem

What is the remainder when 2^16 is divided by 17?

• 0

• 1

• 2

• 16

What is the result of 2^16 mod 17 according to Fermat's Little Theorem?

• 2

• 1

• 3

• 0

What is the result of 2^16 mod 17 according to Fermat's Little Theorem?

• 0

• 1

• 2

• 3

What is the result of 2^16 mod 17 according to Fermat's Little Theorem?

• 2

• 3

• 1

• 0

Why is it important to verify the result of 2^16 mod 17 using a calculator?

• To ensure the calculator is working

• To confirm the theoretical result with a practical calculation

• To find the exact value of 2^16

• To practice using a calculator