Università Roma Tre

Arithmetic functions and their properties:
-Definition and Dirichlet convolution.
-Number and sum of divisors function.
-Möbius function.
-Euler function.

Congruences:
-Sets of residues.
-Polynomial congruences.
-Primitive roots.

Quadratic residues:
-Legendre symbol.
-Quadratic reciprocity.
-Jacobi symbol.

Sums of squares:
-Sums of two squares.
-Number of representations.
-Sums of four squares.
-Sums of three squares.

Continued fractions and diophantine approximation:
-Simple continued fractions.
-Continued fractions and diophantine approximation.
-Infinite simple continued fractions.
-Periodic continued fractions.
-Pell's equation.
-Liouville's Theorem.

Lecture notes

Note di W. Chen
http://www.williamchen-mathematics.info/lnentfolder/lnent.html

An Introduction to the Theory of Numbers by G. H. Hardy, E. M. Wright

M. Fontana, Appunti del corso TN1 (Argomenti della teoria classica dei numeri), http://www.mat.uniroma3.it/users/fontana/didattica/fontana_didattica.html#dispense