Modular Arithmetic and Exponentiation

The video tutorial explains how to solve the problem of finding 11 to the power of 19 modulo 23 using a combination of iterative and factoring methods. It begins by calculating the powers of 11 from 1 to 7 modulo 23, then demonstrates how to use combinations of these powers to simplify the calculation of 11 to the power of 19 modulo 23. The tutorial emphasizes the importance of choosing smaller numbers for easier multiplication and concludes with the final result of the calculation.

What is the main problem discussed in the video?

• Calculating 11 to the power 19 mod 23

• Finding the square root of 23

• Solving linear equations

• Calculating 23 to the power 11 mod 19

Which method is used to solve the problem?

• Substitution method

• Trial and error method

• Iterative and factoring method

• Graphical method

What is 11 to the power 1 mod 23?

• 6

• 13

• 11

• 20

How is 11 to the power 3 mod 23 calculated?

• By subtracting 11 to the power 1 from 11 to the power 2 mod 23

• By dividing 11 to the power 1 by 11 to the power 2 mod 23

• By adding 11 to the power 1 and 11 to the power 2 mod 23

• By multiplying 11 to the power 1 and 11 to the power 2 mod 23

What is the result of 11 to the power 4 mod 23?

• 9

• 5

• 13

• 20

Which combination is used to calculate 11 to the power 5 mod 23?

• 11 to the power 2 and 11 to the power 5

• 11 to the power 3 and 11 to the power 4

• 11 to the power 2 and 11 to the power 3

• 11 to the power 1 and 11 to the power 4

What is the value of 11 to the power 5 mod 23?

• 13

• 5

• 9

• 7

Why is 11 to the power 1 used in calculating 11 to the power 6 mod 23?

• Because it is a smaller number

• Because it is an even number

• Because it is a perfect square

• Because it is a prime number

What is the result of 11 to the power 6 mod 23?

• 5

• 9

• 13

• 7

Which combination is used to calculate 11 to the power 7 mod 23?

• 11 to the power 6 and 11 to the power 1

• 11 to the power 3 and 11 to the power 4

• 11 to the power 4 and 11 to the power 3

• 11 to the power 5 and 11 to the power 2