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Search: id:A156718
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| A156718 |
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Numbers n such that n^2+1=0 mod 13^2. |
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+0
7
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| 70, 99, 239, 268, 408, 437, 577, 606, 746, 775, 915, 944, 1084, 1113, 1253, 1282, 1422, 1451, 1591, 1620, 1760, 1789, 1929, 1958, 2098, 2127, 2267, 2296, 2436, 2465, 2605, 2634, 2774, 2803, 2943, 2972, 3112, 3141, 3281, 3310, 3450, 3479, 3619, 3648, 3788
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OFFSET
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1,1
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COMMENT
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Also, a(n)=169n+-70.
Let n=[A156718] (70,99,239,268,408,437,...,). If A=[A156640] (29,338,985,...,) or A=[156639] (29,58,425) =(n^2+1)/13^2 , Y=26*n, [A156636] (1820,6214,10608,...,) or Y=[A156627] (2574,6968,11362,...,) and X=2*n^2+1 [A156721] (9801,19603,143649,...,) or X=[A156735] (9801,114243,332929,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=70, A=29, Y=1820, X=9801; 9801^2-29*1820^2=1; n=99, A=58, Y=2574, X=19603; 19603^2-58*2574^2=1; n=239, A=338, Y=6214, X=114243; 114243^2-338*6214^2=1; n=268, A=425, Y=6968, X=143649; 143649^2-425*6968^2=1. [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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LINKS
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Vincenzo Librandi, X^2-AY^2=1 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
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FORMULA
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G.f.: (70*x^2 + 29*x + 70)/(x^3 - x^2 - x + 1) [From Alexander R. Povolotsky (pevnev(AT)juno.com), Feb 15 2009]
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EXAMPLE
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70^2+1=0 mod (13^2); 99^2+1=0 mod (13^2); 239^2+1=0 mod (13^2).
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CROSSREFS
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Cf. A156639, A156640, A156636, A156627, A156721, A156735 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A036191 A165632 A136117 this_sequence A007621 A051971 A075004
Adjacent sequences: A156715 A156716 A156717 this_sequence A156719 A156720 A156721
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KEYWORD
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nonn
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AUTHOR
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Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 14 2009
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