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, …

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 …

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 …

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 …

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).

Congratulations! You now have a handle on modular arithmetic. Bonus note for the CS fans: To tie this back to your intuition from CS, it may seem like we have shown that if x%n = a%n and …

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

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 …

Inverses in Modular arithmetic We have the following rules for modular arithmetic: Sum rule: IF a ≡ b(mod m) THEN a + c ≡ b + c(mod m). (3) m) on An inverse to ab ≡ 1(mod m).

For a given positive integer , the relation (mod ) is an equivalence relation on the set of integers. This relation gives rise to an algebraic structure called the integers modulo (usually known as …