Erdős Problem #1131
OPENdatabase updated 2026-01-01
No proof or disproof is known, and it isn't known whether a finite computation could settle it.
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Prizenone
Topicsanalysis, polynomials
Statement in Leannot yet
Solution in Leanno
Original pageerdosproblems.com/1131
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Brutman and Toledano computed the four-node optimum numerically in 1997. We give an independently checkable exact global certificate: the unique nodes are {-1,-sqrt(y),sqrt(y),1}, where 21y^3+9y^2+3y-1=0, and the minimum is algebraic of degree three. This finite result does not settle the asymptotic problem, and no priority claim is made for the exact formulas.
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