On a problem of Favard concerning algebraic integers
C. W. Lloyd‐Smith · Bulletin of the Australian Mathematical Society · 1984
Let α be an algebraic integer of degree n > 1 with conjugates α = α1, α2, …, αn. Let D(α) denote the diameter of {α1, …, αn} and diam . In 1929 Favard showed that diam and that, when n = 2 or 3, the minimal values of diam (α) are less than 2. The author shows that diam and He also finds all algebraic integers a with diam (α) ≤ 2 when n ≤ 5. Similar results are found for D(α) and, in particular, D(α) > 2 when n = 5.