Determination of integer solutions of a system of simultaneous Pell equations (Q1048607)

This paper presents in details the effective resolution of simultaneous generalized Pell equations \[ \begin{cases} x^2 -(2k+1) z^2 = k^2, \\ y^2 -(2\ell +1) z^2 = \ell^2,\end{cases} \] where the parameters \(k\) and \(\ell\) are different positive integers. The method initialized by Baker and Davenport in 1969 involves lower bounds of linear forms in (three) logarithms and the famous Baker-Davenport lemma. Results of computer computation for \(1 \leq k < \ell \leq 100\) are given. Reviewer's remark: The translation from the Russian original paper is not perfect. For example, instead of the ``degree'' of a number field, one finds the ``power'' of a field.