JACOBI'S LAST THEOREM The history of Jacobi-Perron algorithm

Prof. Schweiger states the following in his Mexico City presentation last week:

We take an integer and two numbers of the form:

α + βx + γx²; α; β; γ ∈ ℤ; x³ = n; n ∈ ℕ

With more specifications that I´ll go over in another note, he states that the algorithm he presents produces a unit of the cubic number field.