Fermat's Little Theorem Applications

The video tutorial explains how to find 24 to the power of 38 modulo 7 using Fermat's Little Theorem. It begins by simplifying the base from 24 to 3, as 24 is larger than 7. The theorem is then applied to reduce the exponent, leveraging the fact that 3 and 7 are relatively prime and 7 is a prime number. The calculation is broken down into steps, ultimately finding that 3^38 mod 7 is congruent to 2. The tutorial provides a clear, step-by-step approach to solving the problem using modular arithmetic and Fermat's Little Theorem.

What is the main problem discussed in the video?

• Finding 24 to the power of 38 modulo 7

• Calculating 24 to the power of 7 modulo 38

• Finding 38 to the power of 24 modulo 7

• Calculating 7 to the power of 24 modulo 38

Why is it necessary to reduce 24 modulo 7?

• To make it divisible by 7

• To simplify the calculation

• To increase the number

• To apply a different theorem

What is the remainder when 24 is divided by 7?

• 3

• 4

• 5

• 6

What is the first step in solving the problem using modular arithmetic?

• Reducing 24 modulo 7

• Applying Fermat's Little Theorem

• Calculating 3 squared

• Finding the remainder of 9 divided by 7

What theorem is introduced to solve the problem?

• Pythagorean Theorem

• Euclidean Theorem

• Fermat's Little Theorem

• Binomial Theorem

Why is Fermat's Little Theorem applicable in this problem?

• Because 24 is greater than 7

• Because 3 and 7 are relatively prime

• Because 38 is a large number

• Because 7 is an even number

What is the significance of the number 6 in Fermat's Little Theorem for this problem?

• It is the remainder of 24 divided by 7

• It is the power of 3

• It is the final answer

• It is P minus 1 where P is 7

According to Fermat's Little Theorem, what is 3 to the power of 6 modulo 7?

• 2

• 3

• 0

• 1

How is the power 38 broken down using Fermat's Little Theorem?

• 6 copies of 6 plus 2

• 5 copies of 7 plus 3

• 4 copies of 9 plus 2

• 3 copies of 12 plus 2

What is the purpose of breaking down the power 38 in the calculation?

• To simplify the exponentiation

• To change the base number

• To find a new modulus

• To apply a different theorem