[Verse 1] When p is prime and a's got no common ground With p itself, then something magical is found Take powers of a, raise it up to p minus one The answer mod p is always gonna be just one [Chorus] Fermat's little secret, hiding in the math A to the p minus one equals one on the path When the prime and number share no common part This theorem's gonna work, it's mathematical art One mod p, one mod p, that's the key you see Fermat's little theorem sets the numbers free [Verse 2] Let me show you why this magic always works so well Take your number a and multiply through every cell One times a, two times a, up to p minus one times a Mod p they're just a shuffle of the numbers in our way [Chorus] Fermat's little secret, hiding in the math A to the p minus one equals one on the path When the prime and number share no common part This theorem's gonna work, it's mathematical art One mod p, one mod p, that's the key you see Fermat's little theorem sets the numbers free [Bridge] Multiply them all together, what do you find P minus one factorial on both sides combined Cancel out the factorial, it's safe to do Since the prime can't divide it, the theorem comes through [Verse 3] There's another way to say it, just as sweet and true A to the power p equals a, that formula works too For every single number, this pattern holds its ground In modular arithmetic, this gem is what we've found [Final Chorus] Fermat's little secret, now you know the way A to the p minus one mod p is one today When gcd of a and p equals just one This theorem's always true, the proof is done One mod p, one mod p, mathematical decree Fermat's little theorem, perfect harmony
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