Department of Mathematicscoretheory
ELEMENTARY NUMBER THEORY
MAT 2137
Syllabus
- 01Linear diophantine equation
- 02prime counting function
- 03statement of prime number theorem
- 04Goldbach conjecture
- 05linear congruences
- 06complete set of residues
- 07Chinese remainder theorem
- 08Fermat's little theorem
- 09Wilson's theorem
- 10Number theoretic functions
- 11sum and number of divisors
- 12totally multiplicative functions
- 13definition and properties of the Dirichlet product
- 14the Mobius Inversion formula
- 15the greatest integer function
- 16Euler's phi-function
- 17Euler's theorem
- 18reduced set of residues
- 19some properties of Euler's phi-function
- 20Order of an integer modulo n
- 21primitive roots for primes
- 22composite numbers having primitive roots
- 23Euler's criterion
- 24the Legendre symbol and its properties
- 25quadratic reciprocity
- 26quadratic congruences with composite moduli
- 27Public key encryption
- 28RSA encryption and decryption
- 29the equation Fermat's Last theorem
References
- David M. Burton, Elementary Number Theory, 6th Ed., Tata McGraw-Hill, Indian reprint, 2007.
- Neville Robinns, Beginning Number Theory, 2nd Ed., Narosa Publishing House Pvt. Ltd., Delhi, 2007.
Credits Structure
2Lecture
1Tutorial
0Practical
3Total