NUMBER THEORY [NT-101A]

The course mainly follows content of following courses:

http://www.math.ucsd.edu/~asalehig/NumThe08.html [Major]

while some some contents is to be followed from :

https://math.berkeley.edu/~ribet/115/  [Alternative]

 

 

Course Content

CH-1-Divisibility

  • divisibility theorems, division algorithm, gcd and theorems, Euclidean algorithm, lcm and theorems,  infinite descent method and least integer principle, primes, fundamental theorem of arithmetic/ unique factorization theorem, perfect square, square free, prime number theorem, binomial coefficient and theorems.

Pg-41 [Q-5]

CH-2-Congruences

  • congruences and its theorems; residue class; complete residue class; reduced residue class; Euler’s totient function; Fermat’s theorem; Wilson’s theorem; Fermat’s theorem; solutions of congruences; Chinese remainder theorem[upto 34]

Books

  1. An Introduction to the Theory of Numbers 5th Edition by Ivan Niven (Author), Herbert S. Zuckerman (Author), Hugh L. Montgomery (Author).