This course was based on the book Number Theory Through Inquiry by David Marshall, Edward Odell, and Michael Starbird. The book contains theoretical material accompanied by exercises, largely of theoretical nature.

The following subjects were discussed during the semester:

• divisibility properties of integers

• prime numbers

• modular arithmetic

• fermat’s little theorem, euler’s theorem

• elements of group theory, lagrange’s theorem

• public key cryptography

• polynomial congruences, primitive roots

• quadratic reciprocity

• pythagorean triples

• continued fractions and pell equations

• integers as sums of squares

• arithmetic of elliptic curves