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Search: id:A006702
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| A006702 |
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Solution to a Pellian equation: least x such that x^2 - n y^2 = +- 1.
(Formerly M0120)
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+0
7
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| 1, 1, 2, 1, 2, 5, 8, 3, 1, 3, 10, 7, 18, 15, 4, 1, 4, 17, 170, 9, 55, 197, 24, 5, 1, 5, 26, 127, 70, 11, 1520, 17, 23, 35, 6, 1, 6, 37, 25, 19, 32, 13, 3482, 199, 161, 24335, 48, 7, 1, 7, 50, 649, 182, 485, 89, 15, 151, 99, 530, 31, 29718, 63, 8, 1, 8, 65, 48842
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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When n is a square, the trivial solution x=1, y=1 is taken; otherwise we take the least x that satisfies either the +1 or -1 equation. - T. D. Noe, May 19 2007
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
A. Cayley, Report of a committee appointed for the purpose of carrying on the tables connected with the Pellian equation ..., Collected Mathematical Papers. Vols. 1-13, Cambridge Univ. Press, London, 1889-1897, Vol. 13, pp. 430-443.
C. F. Degen, Canon Pellianus. Hafniae, Copenhagen, 1817.
D. H. Lehmer, Guide to Tables in the Theory of Numbers. Bulletin No. 105, National Research Council, Washington, DC, 1941, p. 55.
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
M. Zuker, Fundamental solution to Pell's Equation x^2 - d*y^2 = +-1
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CROSSREFS
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Cf. A006703, A077232
Sequence in context: A153910 A052532 A006704 this_sequence A129394 A049901 A117715
Adjacent sequences: A006699 A006700 A006701 this_sequence A006703 A006704 A006705
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KEYWORD
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nonn,nice,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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Corrected and extended by T. D. Noe, May 19 2007
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