cp's OEIS Frontend

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.

%I A324601 #7 Aug 01 2019 04:00:38
%S A324601 2,5,12,13,34,70,75,89,179,133,183,182,610,1120,919,2378,1719,2923,
%T A324601 2216,4181,5479,10946,13860,2337,16725,19760,13563,13357,39916,822,
%U A324601 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
%N 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.
%C A324601 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.
%C A324601 For the values k(n) = (a(n)^2 + 1)/m(n), for n >= 3, see A309161.
%C A324601 Many of these values coincide with A305310.
%H A324601 Martin Aigner, <a href="https://doi.org/10.1007/978-3-319-00888-2">Markov's Theorem and 100 Years of the Uniqueness Conjecture</a>, Springer, 2013, p. 58.
%Y A324601 Cf. A002559, A305310, A309161.
%K A324601 nonn
%O A324601 3,1
%A A324601 _Wolfdieter Lang_, Jul 26 2019