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A327337
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Consider primitive solutions (x,y,z) to the system x+y+z = r^2, x^2+y^2+z^2 = s^2, x^3+y^3+z^3 = t^2, with 0<x<=y<=z arranged in order of increasing z; sequence gives z values.
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2
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OFFSET
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1,1
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COMMENTS
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A solution is primitive if it cannot be obtained multiplying another solution by a square greater than 1, i.e., if GCD(x,y,z) is squarefree.
The first two solutions are reported in Choudhry's paper, whose main purpose is providing a parametric solution.
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LINKS
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Table of n, a(n) for n=1..7.
Ajai Choudhry, A diophantine system, arXiv:1908.09742v1 [math.NT], 2019.
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EXAMPLE
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108 + 124 + 129 = 19^2, 108^2 + 124^2 + 129^2 = 209^2, 108^3 + 124^3 + 129^3 = 2305^2.
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CROSSREFS
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The corresponding x and y values are in A327338 and A327339.
Cf. A139266.
Sequence in context: A301551 A297493 A279640 * A305722 A189608 A168067
Adjacent sequences: A327334 A327335 A327336 * A327338 A327339 A327340
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KEYWORD
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nonn,more
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AUTHOR
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Giovanni Resta, Sep 02 2019
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STATUS
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approved
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