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A324601 Unique solution x of the congruence x^2 = -1 (mod m(n)), with m(n) = A002559(n) (Markoff numbers) in the interval [1, floor(m(n)/2)], assuming the Markoff uniqueness conjecture, for n >= 3. 1
2, 5, 12, 13, 34, 70, 75, 89, 179, 133, 183, 182, 610, 1120, 919, 2378, 1719, 2923, 2216, 4181, 5479, 10946, 13860, 2337, 16725, 19760, 13563, 13357, 39916, 822, 26982, 15075, 3952, 162867, 117922, 196418, 249755, 201757, 259304, 86545, 464656, 562781, 651838, 770133, 553093, 1116300, 1354498, 1346269, 56794, 58355, 3087111, 2435532, 166408, 3729600, 4440035, 923756 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

COMMENTS

See the Aigner reference, Corollary 3.17., p. 58. If this congruence is solvable uniquely for integer x in the given interval then the Markoff uniqueness conjecture is true.

For the values k(n) = (a(n)^2 + 1)/m(n), for n >= 3, see A309161.

Many of these values coincide with A305310.

LINKS

Table of n, a(n) for n=3..58.

Martin Aigner, Markov's Theorem and 100 Years of the Uniqueness Conjecture, Springer, 2013, p. 58.

CROSSREFS

Cf. A002559, A305310, A309161.

Sequence in context: A103832 A191368 A085227 * A305310 A039586 A114217

Adjacent sequences:  A324598 A324599 A324600 * A324602 A324603 A324604

KEYWORD

nonn

AUTHOR

Wolfdieter Lang, Jul 26 2019

STATUS

approved

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)