06-07-2014, 09:17 AM
The programme finds the primitive integer solution of Pell’s equation
x^2 – D * y^2 = ± 1
for integer input D and 1 or -1 for solution of the +1 or -1 case respectively.
For input 13 & 1 the programme returns [649, 180, 1] & indeed
649^2 – 13 * 180^2 = 1
Similarly input 13 & -1 returns [18, 5, -1] &
18^2 – 13 * 5^2 = -1
Input 7 & -1 returns 0, indicating that
x^2 – 7 * y^2 = -1
has no integer solutions for x & y.
x^2 – D * y^2 = ± 1
for integer input D and 1 or -1 for solution of the +1 or -1 case respectively.
Code:
1 LBL P
2 STO K
3 1
4 STO F
5 REGZ►A
6 ENTER
7 √x
8 IP
9 STO B
10 STO D
11 STO H
12 x^2
13 -
14 STO I
15 x=0?
16 RTN
17 2
18 RCL* B
19 RCL/ I
20 IP
21 STO C
22 STO G
23 RCL* B
24 1
25 +
26 STO E
27 RCL I
28 1
29 x≠y?
30 GTO P037
31 RCL K
32 x>0?
33 GTO P082
34 RCL A
35 [D,F,-1]
36 RTN
37 0
38 STO J
39 RCL J
40 NOT
41 STO J
42 RCL C
43 RCL* I
44 RCL- H
45 STO H
46 x^2
47 +/-
48 RCL+ A
49 RCL/ I
50 IP
51 STO I
52 1
53 x≠y?
54 GTO P067
55 RCL K
56 x<0?
57 GTO P062
58 RCL J
59 x≠0?
60 GTO P082
61 GTO P067
62 RCL J
63 x=0?
64 GTO P082
65 0
66 RTN
67 RCL B
68 RCL+ H
69 RCL/ I
70 IP
71 STO C
72 RCL* E
73 RCL+ D
74 x<>E
75 STO D
76 RCL C
77 RCL* G
78 RCL+ F
79 x<>G
80 STO F
81 GTO P039
82 RCL A
83 [E,G,K]
84 RTNFor input 13 & 1 the programme returns [649, 180, 1] & indeed
649^2 – 13 * 180^2 = 1
Similarly input 13 & -1 returns [18, 5, -1] &
18^2 – 13 * 5^2 = -1
Input 7 & -1 returns 0, indicating that
x^2 – 7 * y^2 = -1
has no integer solutions for x & y.