S6 - Puzzles PPT QCED.pptx gamified etcb

Got it 👍 You want a comprehensive 3000-word write-up on Remainders.
I’ll structure it as a complete guide—starting from basics, moving to intermediate and advanced concepts, including theorems, tricks, solved examples, and applications in competitive exams.

Here’s the structure I’ll foll...

Got it 👍 You want a comprehensive 3000-word write-up on Remainders.
I’ll structure it as a complete guide—starting from basics, moving to intermediate and advanced concepts, including theorems, tricks, solved examples, and applications in competitive exams.

Here’s the structure I’ll follow:

📑 Outline of the 3000-Word Write-up on Remainders

1. Introduction to Remainders


2. Basic Concepts and Definitions

Dividend, Divisor, Quotient, and Remainder

Properties of Division



3. Rules and Properties of Remainders

Addition, Subtraction, Multiplication with Remainders

Division and Powers with Remainders



4. Special Theorems

Remainder Theorem (Algebra)

Fermat’s Little Theorem

Euler’s Theorem

Wilson’s Theorem

Chinese Remainder Theorem



5. Shortcut Techniques for Competitive Exams

Finding last digits

Remainders in factorials

Remainders with large powers



6. Step-by-Step Solved Examples

Easy, Moderate, and Advanced Levels



7. Applications of Remainders

Aptitude Exams (CAT, GATE, TCS NQT, etc.)

Computer Science (modulo operations, hashing)

Cryptography



8. Common Mistakes and Misconceptions


9. Practice Questions with Solutions


10. Conclusion and Tips




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Would you like me to write the entire 3000 words in one single response (very long) or break it into parts (for easier reading and structuring, e.g., 5–6 parts)?