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A112651
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Numbers k such that k^2 == k (mod 11).
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4
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0, 1, 11, 12, 22, 23, 33, 34, 44, 45, 55, 56, 66, 67, 77, 78, 88, 89, 99, 100, 110, 111, 121, 122, 132, 133, 143, 144, 154, 155, 165, 166, 176, 177, 187, 188, 198, 199, 209, 210, 220, 221, 231, 232, 242, 243, 253, 254, 264, 265, 275, 276, 286, 287, 297, 298
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OFFSET
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1,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = 11*n/2 - 31/4 - 9*(-1)^n/4.
G.f.: x^2*(1+10*x) / ( (1+x)*(x-1)^2 ). (End)
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EXAMPLE
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12 is a term because 12*12 = 144 == 1 (mod 11) and 12 == 1 (mod 11).
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MAPLE
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m = 11 for n = 1 to 300 if n^2 mod m = n mod m then print n; next n
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MATHEMATICA
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Select[Range[0, 300], PowerMod[#, 2, 11]==Mod[#, 11]&] (* or *) LinearRecurrence[ {1, 1, -1}, {0, 1, 11}, 60] (* Harvey P. Dale, Apr 19 2015 *)
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PROG
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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