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Search: id:A070065
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| A070065 |
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Values of x in positive integer solutions of x^2 + y^5 = z^3, listed in increasing order of z. (If a z-value occurs twice, list solutions in increasing order of y.) |
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+0
4
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| 10, 1242, 1024, 5632, 20480, 17920, 37376, 39151, 36599, 15552, 26001, 75000, 124416, 68608, 172800, 209952, 359424, 413343, 579096, 327680, 684288, 1090625, 1306368, 1650240, 1506463, 1529437, 1607445, 1525899, 3637224, 2783744
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OFFSET
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1,1
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EXAMPLE
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The first 5 solutions are (x,y,z) = (10,3,7), (1242,9,117), (1024,16,128), (5632,16,320), and (20480,32,768).
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MATHEMATICA
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For[z=1, True, z++, z3=z^3; For[y=1, (d=z3-y^5)>0, y++, If[IntegerQ[x=Sqrt[d]], Print[{x, y, z}]]]]
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CROSSREFS
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y-values are in A070066, z-values are in A070067.
Sequence in context: A130598 A027879 A015108 this_sequence A013367 A013366 A013364
Adjacent sequences: A070062 A070063 A070064 this_sequence A070066 A070067 A070068
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KEYWORD
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nonn
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AUTHOR
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Dean Hickerson (dean(AT)math.ucdavis.edu) and Dan Asimov(asimov(AT)msri.org), Apr 18 2002
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