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We derive a so-called gap equation for superconductivity in aquasi-one-dimensional (Q1D) layered conductor in a magnetic field, which isparallel to both its conducting plane and its conducting axis. This equationdemonstrates that the orbital destructive effects against superconductivitycannot destroy it, if the perpendicular to the plane coherence length is lessthan the inter-plane distance. On the basis of our results, we suggestarguments that some triplet superconducting phase was indeed discovered inultrahigh magnetic fields in the Q1D superconductor Li$_{0.9}$Mo$_6$O$_{17}$[see Xiaofeng Xu et al., Phys. Rev. Lett., $\bf{102}$, 206602 (2009).] We alsodiscuss a possibility that the above-mentioned superconducting phase can bestable at arbitrary high magnetic fields.

physical review. b./physical review. b

Possible Existence of Superconductivity in the Quasi-One-Dimensional  Conductor Li$_{0.9}$Mo${_6}$O$_{17}$ at Ultrahigh Magnetic Fields, $H \geq 45  \ T$