[Verse 1] Picture a clock face spinning round and round After twelve comes one, that's the pattern found When numbers wrap around at their limit line That's modular arithmetic by design Seven plus eight makes three on a clock of twelve Fifteen becomes three when the numbers shelve [Chorus] Mod n means wrap around, wrap around When you hit the ceiling, come back down A congruent to B when their difference divides By n so cleanly, that's where truth resides Addition and multiplication both obey The modular rules in their wrapping way [Verse 2] If A and B leave the same remainder when You divide by n, they're congruent then The vertical bars mean "divides evenly" N divides A minus B perfectly Twenty-three mod seven equals two Sixteen mod seven gives two also, it's true [Chorus] Mod n means wrap around, wrap around When you hit the ceiling, come back down A congruent to B when their difference divides By n so cleanly, that's where truth resides Addition and multiplication both obey The modular rules in their wrapping way [Bridge] Take each number, find its remainder first Then add or multiply, let the pattern burst The result will match if you compute it whole Modular arithmetic keeps control Fermat whispers secrets from the past A to the P minus one equals one at last [Verse 3] When P is prime and A shares no factors Fermat's Little Theorem never wavers Raise A to the power P minus one Modulo P gives one, the deed is done This ancient truth powers RSA keys Cryptography built on such mysteries [Outro] From infinite numbers to finite frames Modular math transforms the games Hash functions dancing, encryption strong The wrapped-around world where we belong
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