Modular Arithmetic and Remainders

This video tutorial introduces modular arithmetic, explaining how to perform calculations by hand and using a calculator. It covers the concept of modulus as the remainder after division and provides examples to illustrate this. The tutorial also delves into modular exponent rules, verifying them through examples, and concludes with a discussion on the modular exponent power rule. The video aims to equip learners with the skills to perform modular arithmetic and understand related exponent rules.

What is the modulus of 17 when divided by 5?

• 1

• 2

• 3

• 4

How is 15 mod 6 calculated?

• Remainder is 4

• Remainder is 1

• Remainder is 3

• Remainder is 2

What is the result of 35 mod 7?

• 2

• 3

• 1

• 0

How can you determine the modulus of a number using a calculator?

• Add, subtract the whole number, multiply by divisor

• Subtract, divide the whole number, multiply by divisor

• Multiply, subtract the whole number, divide by divisor

• Divide, subtract the whole number, multiply by divisor

What is the remainder when 18,396 is divided by 5?

• 3

• 1

• 2

• 0

What is the modular exponent rule for A^B mod N?

• A raised to B mod N

• A mod B raised to N mod B

• A raised to N mod B

• A mod N raised to B mod N

What is the result of 7^8 mod 5?

• 0

• 3

• 2

• 1

What is the modular exponent power rule?

• A^(B-C) mod N = (A^B mod N)^(C mod N)

• A^(B*C) mod N = (A^B mod N)^(C mod N)

• A^(B*C) mod N = (A^C mod N)^(B mod N)

• A^(B+C) mod N = (A^B mod N)^(C mod N)

What is the result of 3^(2*4) mod 7?

• 0

• 3

• 2

• 1

What is the result of 81 mod 7 raised to the 2nd mod 7?

• 4

• 2

• 1

• 0