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Number Theory: Notes by Anwar Khan Partial Contents These are the handwritten notes. We are very thankful to Mr. Anwar Khan for providing these notes. 1. Number Theory ................................................................... 1 2. Divisibility ........................................................................ 2 3. Euclids Theorem ................................................................. 15 4. Base of Radix Representation .................................................... 19 5. Common Division ................................................................ 21 6. Method of finding great common divisor ......................................... 23 7. G.C.D. more than two integers ................................................... 38 8. Least Common Multiple ......................................................... 39 9. The Linear Diophantine Equation ................................................ 45 10. Theory of Primes ................................................................ 54 11. Composite Number .............................................................. 54 12. Prime Divisor .................................................................... 54 13. Congruence ...................................................................... 61 14. Complete Residue System ........................................................ 85 15. Solutions of the Congruence ..................................................... 102 16. Perfect Number ................................................................. 107 17. Reduce residue System .......................................................... 123 18. Quadratic residue ............................................................... 191 19. Arithmetic Function ............................................................ 205 Available at www.MathCity.org/msc/notes/ If you have any question, ask at www.facebook.com/MathCity.org MathCity.org is a non-profit organization, working to promote mathematics in Pakistan. If you have anything (notes, model paper, old paper etc.) to share with other peoples, you can send us to publish on MathCity.org. For more information visit: www.MathCity.org/participate/ 1
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Page 1: Number Theory: Notes - MathCity.org · Number Theory: Notes by Anwar Khan Partial Contents These are the handwritten notes. We are very thankful to Mr. Anwar Khan for providing ...

Number Theory: Notes

by

Anwar Khan

Partial Contents

These are the handwritten notes. We are very thankful to Mr. Anwar Khan for providingthese notes.

1. Number Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2. Divisibility . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3. Euclids Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

4. Base of Radix Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

5. Common Division . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21

6. Method of finding great common divisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23

7. G.C.D. more than two integers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

8. Least Common Multiple . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

9. The Linear Diophantine Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45

10. Theory of Primes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

11. Composite Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

12. Prime Divisor . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

13. Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61

14. Complete Residue System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

15. Solutions of the Congruence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .102

16. Perfect Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

17. Reduce residue System . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 123

18. Quadratic residue . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 191

19. Arithmetic Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

Available at www.MathCity.org/msc/notes/If you have any question, ask at www.facebook.com/MathCity.org

MathCity.org is a non-profit organization, working to promote mathematics in Pakistan. Ifyou have anything (notes, model paper, old paper etc.) to share with other peoples, you cansend us to publish on MathCity.org.For more information visit: www.MathCity.org/participate/

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