Fermat's Little Theorem Concepts

The video tutorial introduces Fermat's Little Theorem, a fundamental result in number theory with applications in cryptography. The theorem states that if p is a prime number and a is a natural number not divisible by p, then a^(p-1) is congruent to 1 modulo p. The tutorial provides a detailed explanation of the theorem and demonstrates it with an example using specific numbers. The example involves calculating powers and applying modulus to verify the theorem's validity. The video concludes with observations on the example, reinforcing the theorem's application.

What is the primary field of mathematics where Fermat's Little Theorem is a fundamental result?

• Algebra

• Number Theory

• Geometry

• Calculus

In which area of technology is Fermat's Little Theorem particularly significant?

• Cryptography

• Data Science

• Artificial Intelligence

• Quantum Computing

What is the condition for the natural number 'a' in Fermat's Little Theorem?

• a must be greater than p

• a must be even

• a must be odd

• a must not be divisible by the prime p

According to Fermat's Little Theorem, what is the result of a^(p-1) mod p?

• a

• p

• 1

• 0

In the example provided, what is the value of the prime number p?

• 3

• 5

• 7

• 11

What is the chosen value of the natural number 'a' in the example?

• 5

• 2

• 3

• 4

What is the result of 3^4 in the example calculation?

• 81

• 100

• 27

• 64

What is the remainder when 81 is divided by 5?

• 0

• 1

• 2

• 3

Why is the remainder 1 when 81 is divided by 5?

• 81 ends in a 1

• 81 is less than 5

• 81 is a prime number

• 81 is a multiple of 5

What does reducing modulo a number mean?

• Multiplying by the number

• Dividing by the number and keeping the quotient

• Adding the number to the result

• Dividing by the number and keeping the remainder