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Key Concepts
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1. Definition
We say a ≡ b (mod n) if n divides the difference (a - b). This means a and b leave the same remainder when divided by n.
2. Properties
- If a ≡ b (mod n) and c ≡ d (mod n), then:
- a + c ≡ b + d (mod n)
- a - c ≡ b - d (mod n)
- a · c ≡ b · d (mod n)
3. Applications
Modular arithmetic is used in ISBN numbers, crypto-algorithms (like RSA), and circular data structures like clocks.