Tunnell's Theorem gives a partial resolution to the ancient congruent number problem, which asks which whole numbers can be the area of a right triangle with rational side lengths. It supplies a simple, explicitly checkable numerical criterion for whether a given number is a congruent number: failing the criterion unconditionally proves a number is not congruent, while showing the criterion is also sufficient depends on the truth of the Birch and Swinnerton-Dyer conjecture, which remains unproven in general.
Facts
StatementTunnell's theorem gives a partial resolution to the congruent number problem, and a full resolution conditional on the Birch and Swinnerton-Dyer conjecture. 1 Classification
Statement FormCharacterization Theorem 1 Connections
Has Statement Form
In Branch
Source Tunnell's theorem (Wikipedia)
Principal Result Of
Source Jerrold B. Tunnell (Wikipedia)
Sources
1. Tunnell's theorem (Wikipedia)
Lead paragraph
In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton-Dyer conjecture, a full resolution.
References, Tunnell 1983 entry
Tunnell, Jerrold B. (1983), A classical Diophantine problem and modular forms of weight 3/2, Inventiones Mathematicae, 72 (2): 323-334
In Branch: Number Theory, Lead sentence
In number theory, Tunnell's theorem gives a partial resolution to the congruent number problem, and under the Birch and Swinnerton
View the SourceJerrold B. Tunnell (Wikipedia)
Principal Result Of: Jerrold Tunnell, ResearchQuote, Principal Result Of: Jerrold Tunnell, Research
He proved Tunnell's theorem in 1983
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