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, …

This goal of this article is to explain the basics of modular arithmetic while presenting a progression of more difficult and more interesting problems that are easily solved using …

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 …

What is modular arithmetic? When we divide two integers we will have an equation that looks like the following: Sometimes, we are only interested in what the remainder is when we divide A by …

May 17, 2025 · Discover the core principles of modular arithmetic in Algebra II, including congruence, operations, and theorems, to build strong foundational skills.

4. Let's use modular arithmetic (and a little bit of mathematical induction which we'll introduce on the y) to prove a Fermat's little theorem, which states that for any prime and any a 2 N, ap a …

This example illustrates one of the uses of modular arithmetic. Modulo n there are only ever finitely many possible cases, and we can (in principle) check them all. 21

Nov 12, 2025 · Modular arithmetic is important in number theory, where it is a fundamental tool in the solution of Diophantine equations (particularly those restricted to integer solutions).

Modular arithmetic is a way of systematically ignoring differences involving a multiple of an integer. If n is an integer, two integers are equal mod n if they differ by a multiple of n; it is as if …

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 …