Hall's conjecture

Source placement record

Hall's conjecture: for any ε > 0 {\displaystyle \varepsilon >0} {\displaystyle \varepsilon >0}, there is some constant c ( ε ) {\displaystyle c(\varepsilon )} {\displaystyle c(\varepsilon )} such that either y 2 = x 3 {\displaystyle y^{2}=x^{3}} {\displaystyle y^{2}=x^{3}} or | y 2 − x 3 | > c ( ε ) x 1 / 2 − ε {\displaystyle |y^{2}-x^{3}|>c(\varepsilon )x^{1/2-\varepsilon }} {\displaystyle |y^{2}-x^{3}|>c(\varepsilon )x^{1/2-\varepsilon }}.

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Source status: Open
Field: Number theory · General
Record type: Revision-pinned source placement
Verification: Source-index reviewed
Source grade: secondary
Reviewed: 2026-07-27T18:04:33.834Z

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Source trail

Wikipedia list subsection — Exact Number theory › General subsection in the revision-pinned source.
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Pinned source revision 1366281547 — Revision-pinned snapshot from 7/27/2026.