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A179793
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Records of minima of the positive distance d between the eleventh power of a positive integer x and the square of an integer y such that d = x^11 - y^2 (x <> k^2 and y <> k^11).
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12
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23, 747, 8847, 12654, 166831, 484471, 573055, 1248668, 1602775, 8764352, 72820023, 94338007, 143404871, 155195023, 262310000, 1529935249, 4884962400, 19571071932, 146228748359, 318603821009, 635586109888, 1305633968055
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OFFSET
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1,1
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COMMENTS
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Distance d is equal to 0 when x = k^2 and y = k^11.
Conjecture (Artur Jasinski): For any positive number x >= A179794(n), the distance d between the eleventh power of x and the square of any y (such that x <> k^2 and y <> k^11) can't be less than A179793(n).
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LINKS
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MATHEMATICA
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d = 11; max = 1000; vecd = Table[10^100, {n, 1, max}]; vecx = Table[10^100, {n, 1, max}]; vecy = Table[10^100, {n, 1, max}]; len = 1; Do[m = Floor[(n^d)^(1/2)]; k = n^d - m^2; If[k != 0, ile = 0; Do[If[vecd[[z]] < k, ile = ile + 1], {z, 1, len}]; len = ile + 1; vecd[[len]] = k; vecx[[len]] = n; vecy[[len]] = m], {n, 1, 10000000}]; dd = {}; xx = {}; yy = {}; Do[AppendTo[dd, vecd[[n]]]; AppendTo[xx, vecx[[n]]]; AppendTo[yy, vecy[[n]]], {n, 1, len}]; dd
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CROSSREFS
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Cf. A179107, A179108, A179109, A179386, A179387, A179388, A179407, A179408, A179784, A179785, A179786, A179790, A179791, A179792, A179793, A179794, A179795.
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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