Prime Fingerprints: The Unique Factorization Theorem

In this episode, we explore the fundamental theorem of arithmetic—the claim that every integer greater than 1 factors uniquely into primes. We trace its ancient roots in Euclid, unpack why uniqueness matters, see how canonical prime factorizations simplify computation (gcds, LCMs), and peek at real-world impact from cryptography to polynomial rings. We'll also glimpse different proofs and the boundaries of factorization in other mathematical structures.

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