We consider two integers x, y to be the same if x and y differ by a multiple of n, and we write this as x = y (mod n), and say that x and y are congruent modulo n.

In pure mathematics, modular arithmetic is one of the foundations of number theory, touching on almost every aspect of its study, and it is also used extensively in group theory, ring theory, …

Sep 3, 2025 · Modular arithmetic is a system of arithmetic for numbers where numbers "wrap around" after reaching a certain value, called the modulus. It mainly uses remainders to get …

Modular arithmetic is a special type of arithmetic that involves only integers. Since modular arithmetic is such a broadly useful tool in number theory, we divide its explanations into …

Sep 27, 2025 · Modular arithmetic, in its most elementary form, arithmetic done with a count that resets itself to zero every time a certain whole number N greater than one, known as the …

Modular arithmetic is a system of arithmetic for integers, which considers the remainder. In modular arithmetic, numbers "wrap around" upon reaching a given fixed quantity (this given …

Jun 14, 2025 · Explore the fundamentals and advanced concepts of modular arithmetic, a crucial tool in number theory and mathematical physics

The Chinese remainder theorem says that provided n and m are relatively prime, x has a unique residue class modulo the product nm. That is if we divide our number of beer bottles by 42 = 3 …

We therefore confine arithmetic in \ ( {\mathbb Z}_n\) to operations which are well-defined, like addition, subtraction, multiplication and integer powers. We can sometimes cancel or even …

Introduction to Modular Arithmetic 1 Introduction y speaking is the study of integers and their properties. Modular arithmetic highlights the power of remainders when solving problems. In …