Sums of squares of integral multiples of an integral element of real bi-quadratic fields (Q6536856)

For any given positive integer \(m\) and certain totally positive algebraic integers \(\alpha\) of a real biquadratic field \(K\), the author studies the question of when \(m\alpha\) can be represented as a sum of integral squares in \(K\). For the case of real quadratic fields, the corresponding question has been studied by \textit{V. Kala} and \textit{P. Yatsyna} [New York J. Math. 26, 1145--1154 (2020; Zbl 1460.11043)] and \textit{M. Raska} [J. Number Theory 244, 24--41 (2023; Zbl 1518.11035)].