A309161 -id:A309161 - 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.

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

Wolfdieter Lang, Jul 26 2019

nonn

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.

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

Cf. A002559, A305310, A309161.

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.

Views

Author

Keywords

Comments

Links

Crossrefs