Understanding Congruences and Modular Arithmetic

What type of equation is used to find integer solutions on a hyperbola?

• Linear equation

• Quadratic equation

• Exponential equation

• Diophantine equation

When dividing an integer by 7, what is the range of possible remainders?

• 1 to 6

• 0 to 6

• 0 to 5

• 1 to 7

Which operation is not generally valid in modular arithmetic?

• Multiplication

• Division

• Subtraction

• Addition

What does the expression 'A is congruent to B mod n' signify?

• A and B have the same remainder when divided by n

• A and B are in different remainder sets

• A and B are equal

• A is a multiple of B

What is the modulus in the expression 'A is congruent to B mod 7'?

• n

• A

• B

• 7

How can you verify if two numbers are congruent mod n?

• By subtracting them and checking if the result is a multiple of n

• By multiplying them and checking the product

• By dividing them and checking the quotient

• By adding them and checking the sum

What is the remainder when 30 is divided by 9?

• 1

• 0

• 3

• 6

If 35 is congruent to -1 mod 6, what is the remainder when 35 is divided by 6?

• 5

• 1

• 6

• 0

What is a common way to visualize modular arithmetic?

• Using a table

• Using a graph

• Using a clock

• Using a number line

In a clock visualization of modulus 9, what number follows 8?

• 10

• 1

• 0

• 9