If it's 10am and you wait 5 hours, it's 3pm — not 15pm. You just did modular arithmetic.
There is a lot of jargon around this one. Strip it away and the math is genuinely simple. If it's 10am and you wait 5 hours, it's 3pm — not 15pm. You just did modular arithmetic.
a mod n = remainder when a is divided by n. 17 mod 12 = 5.
Hash functions, RSA encryption, error-detecting codes, day-of-week calculators.
Addition and multiplication work modulo n. Division needs care (modular inverse).
Where do programmers use modulo? Indexing circular arrays, even/odd checks, hash tables, time arithmetic.
What's modular exponentiation? Computing (a^b) mod n efficiently — backbone of RSA and Diffie-Hellman.
If you only remember one thing from this post, make it that the inputs matter more than the calculator.