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A061281
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Side of n-th equilateral triangle enclosing at least one point located at integer distances from the vertices.
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6
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112, 147, 185, 224, 273, 283, 294, 331, 331, 336, 370, 403, 441, 448, 485, 520, 546, 555, 559, 560, 566, 588, 592, 637, 645, 662, 662, 672, 691, 735, 740, 784, 806, 819, 849, 882, 896, 925, 965, 970, 993, 993, 1008, 1029, 1040, 1047, 1092, 1110, 1118, 1120, 1132
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OFFSET
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1,1
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COMMENTS
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The equation has many other integer solutions, such as {3,5,7,8}; most of these describe points that lie on the edge of the triangle. - David Wasserman, Jun 10 2002. See A089025.
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REFERENCES
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M. Gardner, Mathematical Circus, Alfred A. Knopf, 1979, p. 65.
L. Pianaro, Pierre Est Encore Perdu, Jouer Jeux Mathematiques, No. 18, Oct 1995, published by French Federation of Mathematics Games.
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LINKS
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FORMULA
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a(n) is the largest term in the n-th quadruple (a, b, c, d) satisfying the triangle equation 3*(a^4 + b^4 + c^4 + d^4) = (a^2 + b^2 + c^2 + d^2)^2.
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EXAMPLE
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The solution (97,185,208,273) of the triangle equation gives rise to the value 273 as the 5th equilateral triangle associated with an interior point at integer distances from the vertices.
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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