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A112654
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Numbers k such that k^3 == k (mod 11).
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2
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0, 1, 10, 11, 12, 21, 22, 23, 32, 33, 34, 43, 44, 45, 54, 55, 56, 65, 66, 67, 76, 77, 78, 87, 88, 89, 98, 99, 100, 109, 110, 111, 120, 121, 122, 131, 132, 133, 142, 143, 144, 153, 154, 155, 164, 165, 166, 175, 176, 177, 186, 187, 188, 197, 198, 199, 208, 209
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OFFSET
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1,3
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COMMENTS
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Nonnegative integers m such that floor(k*m^2/11) = k*floor(m^2/11), where k can assume the values from 4 to 10. See the second comment in A265187. - Bruno Berselli, Dec 03 2015
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LINKS
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FORMULA
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a(n) = a(n-1) + a(n-3) - a(n-4).
G.f.: x^2*(1+9*x+x^2)/((1-x)^2*(1+x+x^2)). (End)
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EXAMPLE
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a(3) = 11 because 11^3 = 1331 == 0 (mod 11) and 11 == 0 (mod 11).
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MAPLE
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m = 11 for n = 1 to 300 if n^3 mod m = n mod m then print n; next n
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MATHEMATICA
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Select[Range[0, 250], PowerMod[#, 3, 11]==Mod[#, 11]&] (* Harvey P. Dale, May 15 2016 *)
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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