Vollst�ndige L�sung der unbestimmten GleichungX 3q+Y3=1 in ganz�n Zahlen

Units generating the ring of integers of complex cubic fields

“…This theorem together with results of Delaunay [5] and Nagell [10] yields: As our main result we will establish the following theorem. …”

“…By a theorem of Delaunay [5] we know that the equation d. This yields a 3 ± d = ±1 or equivalently d = a 3 ± 1 for some integer a.…”

“…By a theorem of Delaunay [5] and Nagell [10] we know that (2) has at most one solution with Y ≥ 0. Suppose (Y, Z) is such a solution, we have aZ 2 −XY = ±Y and bY 2 − XZ = ±Z.…”

“…Let 0 < b < a ∈ Z, a ≤ 50, a and b square-free and gcd(a, b) = 1, with ab 2 ≡ ±1 mod 9, then (a, b) ∈ P with (13,5), (10, 1), (7, 2)}.…”

Remarques sur une classe d’équations indéterminées

“…Pour faire ses r~sultats plus accessibles, Delaunay a publi~ des traduetions de ses m~moires principaux dans le journal Mathematische Zeitschrift; voir [23] et [24]. I1 a aussi publi~ un m~moire particulier sur l'algorithme de rehaussement; voir [25].…”