Introduction to Congruence Modulo n

This video tutorial introduces the concept of congruence modulo n, explaining that every integer belongs to a unique remainder class for a given divisor. It discusses how remainder classes form a partition of integers and how an equivalence relation can be defined from this partition. The video uses modulo 5 to illustrate remainder classes and introduces notation for congruence. It provides a formal definition of congruence modulo n and explains the relationship between congruence and divisibility. A concrete example with numbers 8 and 23 is used to demonstrate these concepts.

What is the technical term for the unique group each integer belongs to for a given divisor?

• Remainder class

• Equivalence set

• Integer partition

• Divisor group

What is the relationship between pairs of numbers in a partition called?

• Divisibility relation

• Equivalence relation

• Equality relation

• Congruence relation

When dividing by 5, which remainder class do the numbers 8 and 23 belong to?

• R = 3

• R = 1

• R = 0

• R = 2

Why are 8 and 23 not equivalent when dividing by 7?

• They have different remainders

• They belong to the same remainder class

• They are both divisible by 7

• They are both prime numbers

How do we express that two numbers are congruent modulo a certain number?

• Using the division symbol

• Using the congruence symbol

• Using the multiplication symbol

• Using the equals sign

What condition must be met for two numbers to be congruent modulo n?

• Their sum is a multiple of n

• Their product is a multiple of n

• Their quotient is a multiple of n

• Their difference is a multiple of n

If a and b are congruent modulo n, what can be said about their difference?

• It is greater than n

• It is less than n

• It is a multiple of n

• It is equal to n

In the example with 8 and 23, what is the value of k if 8 - 23 = k * 5?

• -5

• 5

• 3

• -3

What does the equation 8 = 23 + k * 5 indicate about the numbers 8 and 23?

• 8 is 23 less than a multiple of 5

• 8 is 23 more than a multiple of 5

• 8 is equal to 23

• 8 is a multiple of 23

What is the main topic of the next lesson mentioned at the end of the video?

• Properties of congruence

• Advanced divisibility

• Remainder classes

• Integer partitions