28442 - Number Theory 1

Course Unit Page

SDGs

This teaching activity contributes to the achievement of the Sustainable Development Goals of the UN 2030 Agenda.

Quality education Gender equality

Academic Year 2021/2022

Course contents

Integer partitions. Ferrers diagrams. Euler Theorem about the generating function of the sequence p(n)= number of partitions of n. Gaussian binomial coefficients. Pentagonal numbers and Euler formula. Residues mod n. Euler and Moebius functions and their properties. Modular equations. Quadratic residues and Legendre symbol. Factorization methods. Primality tests. Pythagorean triples. Arithmetic functions. Dirichlet product. Multiplicative and completely multiplicative functions. Cyclotomic polynomial. Distribution function of an arithmetic function. First properties of algebraic integers. 

Readings/Bibliography

Tom M. Apostol: Introduction to Analytic Number Theory - Springer, 2010
Marilena Barnabei - Flavio Bonetti: Elementi di aritmetica modulare - Esculapio, Bologna, 2014

Teaching methods

Teaching at the blackboard.

Office hours

See the website of Marilena Barnabei

See the website of Marta Morigi