Congruence (Number Theory) - Wikipedia
Unknown
Detailed overview with proofs
More resources on Congruences
Modular Arithmetic - Khan Academy
Interactive lessons on congruences
Art of Problem Solving Wiki: Congruences
Comprehensive wiki with problems and solutions
Introduction to Number Theory
Explore number theory with AoPS! Learn about congruences and their applications in this introductory course.
Number Theory and Cryptography
A prominent expert in the number theory Godfrey Hardy described it in the beginning of 20th century as one of the most obviously useless branches of Pure Mathematics”. Just 30 years after his death, an algorithm for encryption of secret messages was developed using achievements of number theory. It was called RSA after the names of its authors, and its implementation is probably the most frequently used computer program in the world nowadays. Without it, nobody would be able to make secure payments over the internet, or even log in securely to e-mail and other personal services. In this course we will start with the basics of the number theory and get to cryptographic protocols based on it. By the end, you will be able to apply the basics of the number theory to encrypt and decrypt messages, and to break the code if one applies RSA carelessly. You will even pass a cryptographic quest! As prerequisites we assume only basic math (e.g., we expect you to know what is a square or how to add fractions), basic programming in python (functions, loops, recursion), common sense and curiosity. Our intended audience are all people that work or plan to work in IT, starting from motivated high school students.
Theory of Numbers
Learn congruences in number theory with this MIT OCW course by Scott Sheffield. Dive into mathematical problem-solving!
mathworld.wolfram.com
MathWorld is Wolfram's comprehensive online math encyclopedia. It offers detailed entries on congruence and modular arithmetic, including definitions, key theorems, worked examples, and links to related topics and references.