Geodesic
On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 319-331

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The work is devoted to the study of Diophantine equation $x^2-y^2(p^{2}-4q)=4t$, where $p=l+u(k^2-1)(l(k^2-1)-2k)$, $q=u(lk^3-2k^2-kl+1)+km+1$, $l=k+m(k^{2}-1)$, numbers $k,m,u$ are nonnegative integers, number $k$ is odd, and the right hand side $4t$ of the equation is sufficiently small positive integer. We give a complete description of solutions of the Diophantine equation.
Mots-clés : diophantine equation, integer solutions, diophantine approximations.
Keywords: generalized Pell's equation, quadratic fields, unit group 
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     title = {On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
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A. A. Korobov; O. A. Korobov. On the discriminant of a quadratic field with intermediate fractions of negative norm and the decomposability of its representing polynomial. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 18 (2021) no. 1, pp. 319-331. http://geodesic.mathdoc.fr/item/SEMR_2021_18_1_a4/