Unique factorization refers to the principle that every integer greater than one can be represented uniquely as a product of prime numbers, up to the order of the factors. This concept is fundamental in number theory and connects closely with the idea that each integer has a distinct 'prime fingerprint,' which is essential for understanding properties like divisibility and congruences. Unique factorization lays the groundwork for many proofs and concepts involving integers, making it a crucial element in the study of mathematical structures.
congrats on reading the definition of unique factorization. now let's actually learn it.