Modular Arithmetic
Middle School
Definition
Integer arithmetic system based on remainder operations (clock arithmetic)
Formulas
a ≡ b (mod n) ⟺ n | (a-b)
(a + b) mod n = ((a mod n) + (b mod n)) mod n
(a · b) mod n = ((a mod n) · (b mod n)) mod n
Examples
Example 1
17 ≡ 5 (mod 12)
Example 2
7⁻¹ ≡ 3 (mod 10)
Applications
Cryptography
Hash functions
Error detection
Related Documents
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