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A172001
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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.
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2
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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FORMULA
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A positive integer n is in this sequence iff its squarefree core A007913(n) belongs to A031398.
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CROSSREFS
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KEYWORD
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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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