s-Дискриминанты и s-уравнение Пелля

The set of all quadratic irrationalities ($s$-discriminants) with decomposition $[q_{0},\overline{q_{1},q_{2},\ldots,q_{2},q_{1},sq_{0}}]$ $(s \ge 2$ — parameter) are described. Theory of Pell $s$-equation is constructed. The inverse problem (reconstruction of $s$-discriminant with the help from continued fraction period’s symmetric part) is solved.

Keywords: $s$-discriminants, Pell $s$-equation, partial periodic continuesfraction, quadratic irrationalities.