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Search: id:A156849
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| 156, 373, 685, 902, 1214, 1431, 1743, 1960, 2272, 2489, 2801, 3018, 3330, 3547, 3859, 4076, 4388, 4605, 4917, 5134, 5446, 5663, 5975, 6192, 6504, 6721, 7033, 7250, 7562, 7779, 8091, 8308, 8620, 8837, 9149, 9366, 9678, 9895, 10207, 10424
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OFFSET
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1,1
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COMMENT
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Let n=[A156849] (156,373,685,902,...,) =n^2-2=0 mod (23^2). If A=[A156841] (46,263,1538,3871,.,) = 529*n^2-312*n+46 or A=[156842] (263,46,887,2787) =(529*n^2-746*n+263 , Y=23*n, or [A156845] (3588,15755,27922,...,) = 12167*n-8579, or Y=[A156846] (8579,20746,32913,...,) =12167*n-3588, and X=279841*n^2-165048*n+24335 [A156843] (24335,139128,813603,...,) or X=[A156844] =279841*n^2-394634*n+139128 (139128,24335,469224,1473795,...,) , we have for all terms, Pell's equation X^2-A*Y^2=1. Example: For n=156, A=46, Y=3588, X=24335, 24335^2-46*3588^2=1 ; n=373, A=263, Y=8579, X=139128; 139128^2-263*8579^2=1; n=685, A=887, Y=15755, X=469224; 469224^2-887*15755^2=1; n=902, A=1538, Y=20746, X=813603; 813603^2-1538*20746^2=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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EXAMPLE
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156^2-2=0 mod (23^2); 373^2-2=0 mod (23^2); 685^2-2=0 mod (23^2); 10424^2-2=0 mod (23^2);
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CROSSREFS
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Cf. A156845, A156846
Cf. A156846, A156845, A156844, A156843, A156842, A156841 [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Feb 20 2009]
Sequence in context: A166397 A065709 A037983 this_sequence A106056 A043356 A038476
Adjacent sequences: A156846 A156847 A156848 this_sequence A156850 A156851 A156852
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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 17 2009
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