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A230962
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Values of x such that x^2 + y^2 = 73^n with x and y coprime and 0 < x < y.
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2
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3, 48, 296, 721, 10072, 213785, 1958709, 7613760, 21165597, 894454032, 12278087704, 59926173839, 62518379032, 3374316625735, 58552907681096, 416603004343680, 1261259807092797, 10231862403603888, 255781764375436389, 2697529798981443601, 11543491568219853608
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OFFSET
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1,1
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COMMENTS
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The corresponding y-values are in A230963.
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LINKS
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FORMULA
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a(n) = min(abs(Re((3+8i)^n)), abs(Im((3+8i)^n))).
a(n) = abs(Re(3+8i)^n) if and only if 1/4 < frac(n*arctan(8/3)/Pi) < 3/4.
(End)
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EXAMPLE
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a(3) = 296 because 296^2 + 549^2 = 389017 = 73^3.
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MAPLE
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f:=n -> min([abs@Re, abs@Im]((3+8*I)^n)):
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MATHEMATICA
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Table[Select[PowersRepresentations[73^n, 2, 2], CoprimeQ@@#&][[1, 1]], {n, 1, 40}] (* Vincenzo Librandi, Mar 02 2014 *)
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PROG
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(Python)
from sympy import I, re, im
print([min(abs(re((3 + 8*I)**n)), abs(im((3 + 8*I)**n))) for n in range(1, 31)]) # Indranil Ghosh, Mar 31 2017, after formula by Robert Israel
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CROSSREFS
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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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