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A172001
Nonsquare positive integers n such that Pell equation y^2 - n*x^2 = -1 has rational solutions but the norm of fundamental unit of quadratic field Q(sqrt(n)) is 1.
2
34, 136, 146, 178, 194, 205, 221, 305, 306, 377, 386, 410, 466, 482, 505, 514, 544, 545, 562, 584, 674, 689, 706, 712, 745, 776, 793, 802, 820, 850, 866, 884, 890, 898, 905, 1154, 1186, 1202, 1205, 1220, 1224, 1234, 1282, 1314, 1345, 1346, 1394, 1405, 1469
OFFSET
1,1
COMMENTS
If the fundamental unit y0 + x0*sqrt(n) of Q(sqrt(n)) has norm -1, then (x0,y0) represents a rational solution to Pell equation y^2 - n*x^2 = -1. For n in this sequence, rational solutions exist but not delivered by the fundamental unit.
FORMULA
A positive integer n is in this sequence iff its squarefree core A007913(n) belongs to A031398.
CROSSREFS
Set difference of A000415 and its subsequence A172000.
Set difference of A087643 and its subsequence A022544.
Squarefree terms form A031398.
Odd terms form A249052.
Sequence in context: A334648 A044366 A044747 * A303302 A158062 A141127
KEYWORD
nonn
AUTHOR
Max Alekseyev, Jan 21 2010
EXTENSIONS
Edited by Max Alekseyev, Mar 09 2010
STATUS
approved