The Pell equation, by Edward Everett Whitford.

54

THE PELL EQUATION

Hence, for
P1 = 1,
we have
v1 < U < 2vl; U = v1 + V2;
Ql(Vl, v2) = 312 - 2vv2 - 4v22 = 1.
For
P2 = 1,
we have
V2 < v1 < 2,2; V1 = V2 + v3;
Q2(v2, v3) = 3v22 + 4v2V3 + 3v32 = 1.
For
P3= 1,
we have
v3 < v2 < 2v3; v2 = v3 -+ 4;
Q3(v3, v4) = 4v32 - 2v34 - 3v42 = 1.
For
P4 = 1,
we have
V4 < V3 < 2V4; V3 = V4 + v5;
Q4(v4, v5) = - v42 - 6v4v5 + 4v52 = 1.
For
P5 = 6,
we have
6v5 < v4 < 7v5; v4 = 6v5 + V6;
Q5(V5, V6) = 4v52 - 6v56 - v62 = 1.
For
P6= 1,
we have
v6 < v5 < 2v6; v5 = v6 + v7;
Q6(v6, V7) = - 3v62 + 2v6v7 + 4v72 = 1.
For
P7 = 1,
we have
v7 < v6 < 2v7; v6 = V7 + V8;
Q7(V7, V8) = 3v72 - 47V8 - 3V2 = 1.
For
P8 = 1,
we have
V8 < V7 < 2v8; v7 = Vs + v9;
Q8(v8, Vg) = - 482 + 2V8v9 + 3v92 = 1.