## Integer and modular arithmetic

### Teaching unit

### Description

### Objectives

To acquire and to use fluently the mathematical, both language oral and written, being rigorous in the formalization and structure of a royal problem in format of mathematical problem.

To be able to apply the knowledge, methods and algorithms to situations and concrete problems of the area of Mathematics and of the Computer science.

To acquire and to apply, of autonomous form and to interdiscipline, new concepts and methods related to the subject and to use adequately the usual terminology of the subject.

To handle correctly the bibliography and the available sources of information to reinforce and to extend knowledge as well as couple to extend the aptitude to consider and solve in a mathematical way diverse problems that could appear and to be related to the Algebra.

To use diverse technological tools (as IT software) that facilitate the resolution of mathematical problems and to understand the limitations of the above mentioned tools.

To be capable of being employed at equipment to solve questions and problems related to the studied matter.

To recognize and to understand some of the capacities, aptitudes and knowledge that the subject contributes for the development of the professional profile of the Engineer in Computer science in Technologies of the Information.

### Subjects

#### Lecture topics

- the integer
- Divisibility
- Greatest common divisor and least common multiple
- Prime numbers. Factorization
- Congruences
- The integer modulo n. Arithmetic Zn
- Invertible elements in Zn
- Euler function

#### Laboratory topics

- Applications to cryptography