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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 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.)