# Réponse finale obtenue du bot:
response = « Here is a course outline on Number Theory:
**Course Title:** Number Theory: Properties of Integers, Famous Theorems and Conjectures, and Cryptography
**Course Description:** This course provides an introduction to the fascinating world of number theory, exploring the properties of integers, famous theorems and conjectures, and their applications in cryptography.
**Course Objectives:**
* Understand the fundamental concepts and results in number theory
* Learn about the properties of integers, including divisibility, primality, and congruences
* Study famous theorems and conjectures in number theory, such as Fermat’s Last Theorem and the Riemann Hypothesis
* Explore the applications of number theory in cryptography, including RSA encryption and digital signatures
**Course Outline:**
**Week 1-2:** Introduction to Number Theory
* Definition and importance of number theory
* Basic properties of integers (divisibility, primality, congruences)
* Introduction to modular arithmetic
**Week 3-4:** Divisibility and Primality
* Euclidean algorithm for finding the greatest common divisor
* Fundamental theorem of arithmetic: every integer can be uniquely represented as a product of prime numbers
* Properties of prime numbers (e.g. infinitude, uniqueness)
**Week 5-6:** Congruences and Diophantine Equations
* Introduction to congruences and their properties
* Linear and quadratic Diophantine equations
* Applications in cryptography (e.g. RSA encryption)
**Week 7-8:** Famous Theorems and Conjectures
* Fermat’s Last Theorem: a proof by Andrew Wiles
* The Riemann Hypothesis: its importance and implications for cryptography
* Other famous theorems and conjectures in number theory (e.g. Dirichlet’s theorem, the prime number theorem)
**Week 9-10:** Cryptography and Number Theory
* Introduction to public-key cryptography
* RSA encryption and digital signatures
* Applications of number theory in cryptography: elliptic curves, lattice-based cryptography
**Assessment:**
* Homework assignments (40%)
* Midterm exam (20%)
* Final project on a topic related to number theory or cryptography (30%)
* Class participation and attendance (10%)
**Recommended Textbook:**
* « A Course in Number Theory » by Henryk Iwaniec and Emmanuel Kowalski
* « Number Theory and Its Applications » by Richard A. Mollin
**Additional Resources:**
* Online resources: Wolfram Alpha, Mathway, Khan Academy
* Video lectures: 3Blue1Brown (YouTube), MIT OpenCourseWare (edX)
This course outline provides a comprehensive introduction to number theory, covering its fundamental concepts and results, as well as its applications in cryptography. The course is designed for undergraduate students with a background in mathematics or computer science. »