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What is modular arithmetic?

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Quick answer

Modular arithmetic is math that 'wraps around' after reaching a set value, like a clock returning to 1 after 12. It's the arithmetic of remainders, and it quietly powers digital clocks, calendars, and modern cryptography. Numbers wrap around a fixed 'modulus,' as hours wrap around 12.

Key things to understand

  1. Numbers wrap around a fixed 'modulus,' as hours wrap around 12.
  2. It focuses on the remainder left after division.
  3. 9 + 5 on a 12-hour clock gives 2, not 14.
  4. It underpins error-checking codes, hashing, and encryption.
  5. It is a foundation of number theory.

People also ask

What is a real-world example of modular arithmetic?
A clock: 3 hours after 11 o'clock is 2, because the hours wrap around after 12 — that's arithmetic modulo 12.
Why does cryptography use modular arithmetic?
Wrapping operations make it easy to scramble numbers and hard to reverse without a key, which helps secure online communication.
What does 'mod' mean?
It's the remainder after division: 17 mod 5 is 2, because 17 divided by 5 leaves 2 left over.