KnowraUnique factorizationLinked fromLinked fromThe 8 pages that link to Unique factorization, each with the reason it gives.All 8Related 4Narrower topic 1Compared with 3Fermat's Last TheoremRelated: Classical attempts extend factorization into larger rings, where uniqueness can fail.Richard DedekindRelated: Ideals restore unique factorization when algebraic integers themselves lack it.Ring of integersCompared with: Its failure in some rings motivated the shift from elements to ideals.Unique factorization domainNarrower topic: This property is the defining condition imposed on elements of the domain.Dedekind domainCompared with: A nontrivial ideal class group obstructs unique factorization of elements.Ernst KummerRelated: Its failure in cyclotomic rings motivated Kummer’s ideal numbers.Ramanujan–Nagell equationRelated: Factoring expressions involving x and √−7 requires care because unique factorization can fail.Stark–Heegner theoremCompared with: For these quadratic integer rings, class number one is equivalent to unique factorization of elements.