# Réponse finale obtenue du bot:
response = « **Course Title:** The Theory of Numbers: Properties, Theorems, and Conjectures
**Course Overview:** This course covers the fundamental concepts and results in number theory, including properties of integers, famous theorems and conjectures, and applications to cryptography.
**Course Objectives:**
1. Understand the basic properties of integers, such as divisibility, primality, and congruences.
2. Learn about famous theorems in number theory, such as Fermat’s Last Theorem and the Prime Number Theorem.
3. Study conjectures that have significant implications for number theory, such as the Riemann Hypothesis.
4. Explore the connection between number theory and cryptography, including public-key encryption algorithms like RSA.
**Course Outline:**
**Week 1:** Introduction to Number Theory
* Overview of number theory
* Properties of integers:
+ Divisibility
+ Primality
+ Congruences
* Examples and exercises
**Week 2-3:** Theorems in Number Theory
* Fermat’s Last Theorem (FLT)
+ Statement and proof outline
+ Applications to cryptography
* Prime Number Theorem (PNT)
+ Statement and proof outline
+ Implications for number theory and cryptography
**Week 4-5:** Conjectures in Number Theory
* Riemann Hypothesis (RH)
+ Statement and significance
+ Attempts at a proof
* Other conjectures:
+ Goldbach’s Conjecture
+ Twin Prime Conjecture
**Week 6-7:** Cryptography using Number Theory
* Introduction to public-key encryption
* RSA algorithm:
+ Principle of operation
+ Security based on number theory
* Other cryptographic applications of number theory:
+ Diffie-Hellman key exchange
+ Elliptic Curve Cryptography (ECC)
**Week 8:** Review and Applications
* Review of major concepts and theorems
* Applications to real-world problems:
+ Computer security
+ Data encryption
+ Secure communication protocols
**Assessment:**
* Homework assignments (40%)
* Midterm exam (20%)
* Final project or presentation (30%)
* Quizzes and class participation (10%)
**Prerequisites:** None, although a background in algebra and calculus is recommended.
**Target Audience:** Students with an interest in mathematics and computer science, particularly those who want to learn about the fundamental principles of number theory and its applications to cryptography. »