A384440 - OEIS

A384440

Array of triples (x,y,z) of minimal (positive) solutions of the cubic Pell equation x^3 + n*y^3 + n^2*z^3 - 3*n*x*y*z = 1, read by rows.

%I #26 Jun 05 2025 08:39:24

%S 1,0,0,1,1,1,4,3,2,5,3,2,41,24,14,109,60,33,4,2,1,1,0,0,4,2,1,181,84,

%T 39,89,40,18,9073,3963,1731,94,40,17,29,12,5,5401,2190,888,16001,6350,

%U 2520,324,126,49,55,21,8,64,24,9,361,133,49

%N Array of triples (x,y,z) of minimal (positive) solutions of the cubic Pell equation x^3 + n*y^3 + n^2*z^3 - 3*n*x*y*z = 1, read by rows.

%C Given n, n!=k^3, there are infinitely many solutions, and all other solutions can be derived from the minimal solution pair by a recurrence relation. See Wolfe, pages 359-369.

%D Clyde Lynne Earle Wolfe, On the Indeterminate Cubic Equation X^3 + Dy^3 + D^2z^3 - 3Dxyz, University of California Press, 1923, pp. 359-369.

%H Xianwen Wang, <a href="/A384440/b384440.txt">Table of n, a(n) for n = 1..6000</a>

%e For n=5, the minimal positive solution is (41, 24, 14), so a(13)=41, a(14)=24, a(15)=14.

%e The array begins:

%e 1, 0, 0,

%e 1, 1, 1,

%e 4, 3, 2,

%e 5, 3, 2,

%e 41, 24, 14,

%e 109, 60, 33,

%e ...

%K nonn,tabf

%O 1,7

%A _Xianwen Wang_, May 29 2025

%E Name edited by _Michel Marcus_, Jun 03 2025