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A096545
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Ordered z such that, for 0<x<y<z, the primitive quadruples (x,y,z,w) satisfy x^3 + y^3 + z^3 = w^3.
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7
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5, 8, 17, 18, 21, 22, 27, 33, 37, 37, 40, 41, 44, 49, 53, 54, 57, 61, 64, 65, 66, 69, 69, 70, 72, 74, 75, 78, 79, 79, 79, 84, 85, 86, 86, 87, 89, 90, 92, 96, 97, 97, 97, 99, 101, 102, 102, 104, 105, 108, 114, 116, 118, 121, 122, 123, 124, 124, 128, 131, 136, 136, 137
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OFFSET
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1,1
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COMMENTS
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For corresponding values w see A096546.
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REFERENCES
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Y. Perelman, Solutions to x^3 + y^3 + z^3 = u^3, Mathematics can be Fun, pp. 316-9 Mir Moscow 1985.
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LINKS
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EXAMPLE
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21 and 22, for instance, are terms because we have: 18^3 + 19^3 + 21^3 = 28^3 and 4^3 + 17^3 + 22^3 = 25^3.
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MATHEMATICA
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s[w_] := Solve[0 < x < y < z && x^3 + y^3 + z^3 == w^3 && GCD[x, y, z, w] == 1, {x, y, z}, Integers];
xyzw = Reap[For[w = 1, w <= 200, w++, sw = s[w]; If[sw != {}, Print[{x, y, z, w} /. sw; Sow[{x, y, z, w} /. sw ]]]]][[2, 1]] // Flatten[#, 1]&;
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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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