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Modular Arithmetic

★★★☆☆High School

📖Definition

Modular arithmetic is a system based on remainders from division. Also called clock arithmetic.

📐Formulas

a ≡ b ±odn ⇔ n | (a - b)

Definition of congruence

(a + b) mod n = ((a mod n) + (b mod n)) mod n

Addition modular property

(a × b) mod n = ((a mod n) × (b mod n)) mod n

Multiplication modular property

✏️Examples

예제 1

Find 17 mod 5.

예제 2

Find 2^10 mod 7.

Applications

Cryptography

RSA encryption

Hash Functions

Hash tables

Error Detection

Checksums, ISBN

🔗Related Documents

Prerequisites

#모듈러#나머지#modular#congruence