Fermat's Little Theorem Concepts

This video introduces a modular arithmetic trick using Fermat's Little Theorem. It explains the concept of co-prime numbers and demonstrates how to apply the theorem with examples, such as calculating 2^35 mod 17 and 4^532 mod 11. The video emphasizes the usefulness of finding powers that are congruent to one, simplifying complex calculations.

What is recommended before watching this video?

• Practicing basic arithmetic

• Studying Fermat's Last Theorem

• Watching previous videos in the series

• Reading a textbook on modular arithmetic

What is the main focus of this video?

• Advanced calculus

• Fermat's Last Theorem

• Fermat's Little Theorem

• Basic arithmetic operations

What does Fermat's Little Theorem state?

• a^(p-1) is congruent to 0 modulo p

• a^(p-1) is congruent to a modulo p

• a^(p-1) is congruent to p modulo a

• a^(p-1) is congruent to 1 modulo p if a and p are co-prime

What does it mean for two numbers to be co-prime?

• They are both even numbers

• They are both prime numbers

• They have only one as a common factor

• They have no common factors

Which of the following pairs are co-prime?

• 5 and 8

• 9 and 12

• 6 and 9

• 4 and 10

In the example with numbers 2 and 5, what is the result of 2^4 mod 5?

• 3

• 0

• 1

• 2

Why is Fermat's Little Theorem useful?

• It is used in calculus

• It helps in solving linear equations

• It simplifies calculations by reducing large powers

• It is a fundamental theorem in geometry

What is the remainder when 2^35 is divided by 17?

• 8

• 2

• 16

• 1

What is the remainder when 4^532 is divided by 11?

• 10

• 6

• 5

• 1

What should you do if you found Fermat's Little Theorem useful?

• Watch the next video for more advanced tools

• Rewatch this video

• Practice more problems

• Read a book on number theory