# Modular Arithmetic YouTube Lecture Handouts

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## Modular Arithmetic

Simply Looking at the Face of Clock

Why Bother? - Shortcuts to Several Problems

• Remainder Problems (Simple)
• LCM
• Chinese Remainder Theorem
• Remainders of Exponentiations: ?
• Last Digit Problems:
• Modular Arithmetic
• Euler՚s and Fermat՚s Little Theorem
• Wilsons Theorem
• More Motivations – Reducing Big Numbers
• Time Problems
• A train coming at 3 pm is delayed 16 hours, what time will it come?

Face of a Clock

## Addition and Subtraction of Congruence՚S

• Find last digit of: 2403 + 791 + 688 + 4339
• Remainder of

## Application of Multiplication- Example-2/3

• Find the remainder of
• There are 44 boxes of chocolates with 113 chocolates in each box. If you sell the chocolates by dozens, how many will be leftover?

## Application of Exponentiation Example – 4/5

• Find the last digit of .
• Find the r

## Division of Congruence՚S: Never Divide, Think from Basics

• – Divide by 2
• (5 and 2 are coprime) - Divide by 2

## Combining Congruence՚S

Example - 6

• 3 professors begin courses of lectures on Monday, Tuesday, Wednesday and announce their intentions of lecturing at intervals of 2,3, 4 days respectively. If there are no lectures on Saturday, after how many days will all professors omit a lecture together?

## Concept of Multiplicative Inverse

• b is multiplicative inverse of a mod N
• a is multiplicative inverse of b mod N

## Summary

• don՚t do division without writing out basic equation

## Next - Faster Solutions to Exponent Problems

• Find the remainder
• Euler and Fermat՚s Little Theorem
• Wilsons Theorem

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