Syllabus
1. Diophantine approximations (approximating real numbers by fractions).
2. Geometry of numbers (lattice points, Minkowski's theorem on convex body).
3. Congruences and residues (quadratic residues).
4. Prime numbers (estimates of Chebyshev and Mertens).
5. Integer partitions (Euler's pentagonal identity).
6. Diophantine equations (Pell equation, FLT for n=4 and for polynomials).
Annotation
1. Diophantine approximations.
2. Geometry of numbers.
3. Congruences and residues.
4. Prime numbers.
5. Integer partitions.
6. Diophantine equations.