Fermat's Little Theorem Concepts

The video tutorial explains Fermat's Little Theorem, which states that if P is a prime number and the GCD of a and P is 1, then a^(P-1) is congruent to 1 mod P. The proof involves considering a set of numbers and showing they are incongruent modulo P. By relating the product of these numbers to a factorial, the proof concludes using Wilson's theorem, demonstrating the theorem's validity.

What is the main condition for Fermat's Little Theorem to hold?

• P must be a composite number.

• The GCD of a and P must be greater than 1.

• a must be a prime number.

• P must be a prime number.

In Fermat's Little Theorem, what is the result of a^(P-1) mod P?

• 0

• a

• P

• 1

What is the purpose of considering the set S in the proof?

• To find the sum of elements.

• To demonstrate congruence of elements.

• To calculate the factorial of P.

• To show incongruence of elements modulo P.

What does the set S consist of in the proof?

• a, 2a, 3a, ..., (P-1)a, Pa

• 0, 1, 2, ..., P-1

• 1, 2, 3, ..., P

• a, a^2, a^3, ..., a^(P-1)

Why can't P divide a in the proof?

• Because a is a prime number.

• Because the GCD of a and P is 1.

• Because a is greater than P.

• Because P is a composite number.

What is the significance of the set S' in the proof?

• It is used to find the product of elements.

• It represents the residues modulo P.

• It is used to calculate the sum of elements.

• It is used to demonstrate congruence.

What does the proof show about the elements of set S?

• They are all equal to a.

• They are all incongruent modulo P.

• They are all congruent modulo P.

• They are all equal to P.

What does the congruence of K times a and L times a imply?

• P divides a.

• K and L are both prime.

• P divides K minus L.

• K and L are equal.

What does the proof use to show incongruence of elements?

• The sum of elements.

• The definition of congruence modulo P.

• The power of a.

• The factorial of P.

What is the role of the GCD in the proof?

• To ensure P does not divide a.

• To calculate the power of a.

• To show that P divides a.

• To demonstrate congruence.