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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
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.
CROSSREFS
KEYWORD
nonn
AUTHOR
Wolfdieter Lang, Jul 26 2019
STATUS
approved