# Congruence Modulo n Multiplication Proof - Clever Proof | Summary and Q&A

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January 26, 2019
by
The Math Sorcerer
Congruence Modulo n Multiplication Proof - Clever Proof

## TL;DR

Understanding the relationship between congruency modulo N, the ability to group numbers with a particular module, and the application of the if-then statement in proving congruency of two different numbers modulo N.

## Key Insights

• 🙅 Modular arithmetic involves understanding congruency between numbers modulo N and utilizing multiples.
• ❓ The proof technique discussed in the content follows an if-then statement structure.
• 👻 The clever trick of inserting a connecting piece simplifies the calculation and allows for the extraction of common factors.
• ❓ This proof technique is elegant and can be applied in various mathematical proofs.
• 🙅 Understanding the concept of congruency modulo N is crucial in modular arithmetic.
• 🧑‍🏭 The ability to manipulate equations and extract common factors is a valuable skill in mathematical proofs.
• ❓ The if-then statement structure is commonly used in mathematical reasoning.

## Transcript

what's going on this problem we're going to prove that if you have a congruent to B modulo N and C you can grew with the D module and then AC is congruent to BD module and it's kind of cool it's kind of if-then statement okay so typically in these types of problems you start by assuming this right and then you just have to show this is true so we'l... Read More

### Q: What is the main objective of the proof technique discussed in the content?

The main objective is to prove that if two conditions of congruency modulo N are true, then the congruency of two different numbers modulo N is also true.

### Q: How does the proof technique begin?

The proof begins by assuming congruency between the numbers modulo N and breaking it down into separate equations that represent the concept of congruency.

### Q: What is the purpose of inserting a connecting piece and rearranging the equation?

The purpose is to simplify the calculation by introducing the connecting piece and rearranging the equation in a way that allows for the extraction of common factors.

### Q: How is the congruency of two different numbers modulo N proven?

By applying the clever trick of inserting the connecting piece, the proof demonstrates that the resulting equation is a multiple of N, proving the congruency of the two numbers modulo N.

## Summary & Key Takeaways

• The content discusses a proof technique in modular arithmetic involving congruency and multiples.

• It explains the process of assuming congruency between two numbers modulo N, and breaking it down into multiple steps.

• The proof utilizes a clever trick of inserting a connecting piece to simplify the calculation and demonstrate congruency.