## Basic Number Theory - MA523 (Fall 2016)

The syllabus for this course reads as follows: Infinitude of primes, discussion of the Prime
Number Theorem, infinitude of primes in
specific arithmetic progressions, Dirichlet's
theorem (without proof). Arithmetic functions, Mobius inversion
formula. Structure of units modulo n, Euler's phi function. Congruences, theorems of Fermat and Euler,
Wilson's theorem, linear congruences,
quadratic residues, law of quadratic
reciprocity. Binary quadratics forms, equivalence,
reduction, Fermat's two square theorem,
Lagrange's four square theorem. Continued fractions, rational approximations,
Liouville's theorem, discussion of Roth's
theorem, transcendental numbers,
*transcendence of e and π*. Diophantine equations - Brahmagupta's
equation (also known as Pell's equation), Fermat's method of descent,
discussion of the Mordell equation.

**Classes are held on Mondays and Thursdays in LT-203 from 2pm to 3.30pm. All are welcome. **

- There was a seminar talk on 29th October, in which Amit Patra explained the proof of
**Agrawal-Kayal-Saxena Theorem**. Some photos from the seminar: here, here and here.

- There was a seminar talk on 30th October, in which Dibyendu Biswas explained the proof of
**Brun's Theorem**, which states that the sum of the reciprocals of twin primes is finite.