The Stark-Heegner Theorem identifies the exact nine positive whole numbers d for which the ring of integers of the imaginary quadratic field generated by the square root of negative d has unique factorization, equivalently has class number one: 1, 2, 3, 7, 11, 19, 43, 67 and 163. Proved by Kurt Heegner in 1952 in a proof initially doubted on a technical point later confirmed correct, and independently by Harold Stark and by Alan Baker, it resolved Gauss's longstanding class number one problem for imaginary quadratic fields.
Facts
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Statement FormCharacterization Theorem 1 Connections
Has Statement Form
Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
In Branch
Source Stark-Heegner theorem (Wikipedia)
Sources
1. Wikipedia: Stark-Heegner theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
The class number of Q ( d ) ({\sqrt {d}})} is one if and only if the ring of integers of Q ( d ) ({\sqrt {d}})} is a principal ideal domain.
2. Stark-Heegner theorem (Wikipedia)
History section
Harold Stark published a proof in 1967
In Branch: Number Theory, Lead sentence
In number theory, the Heegner theorem or Stark-Heegner theorem establishes the complete list of the quadratic imaginary number fie
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