[Verse 1] Pierre de Fermat had a hunch one day Prime numbers dance in a special way Take any number, call it little a If it shares no factors with prime p When you raise a to the power of p minus one Divide by p and watch what becomes The remainder's always gonna be one This pattern holds for every prime sum [Chorus] Little theorem, big revelation A to the p-1 mod p equals one When the gcd is one, no hesitation Fermat's magic formula's never done Prime p calling, numbers falling Into perfect modular line A to the p-1, that's the calling Congruent to one every time [Verse 2] Here's the proof that makes it crystal clear Take multiples: a, two-a, three-a here Up to p-1 times a, all appear As permutations when mod p draws near Multiply them all together now The factorial times a to the power Equals factorial, mathematics shows Cancel both sides, watch the theorem flower [Chorus] Little theorem, big revelation A to the p-1 mod p equals one When the gcd is one, no hesitation Fermat's magic formula's never done Prime p calling, numbers falling Into perfect modular line A to the p-1, that's the calling Congruent to one every time [Bridge] There's another way to state this truth A to the p congruent to a For any number, here's the proof Modular arithmetic shows the way [Outro] Prime numbers hold this secret tight Fermat glimpsed this perfect sight Modular math reveals the pattern Little theorem, foundations matter
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