(12C) Sums of Two Squares

[Gamo]

Which whole numbers are expressible as sums of two (integer) squares?

This program solve the Sums of Two Squares. [ X^2 + Y^2 = N ]

Given N program will find pair of X,Y that equal to N

where X ≤ Y

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Procedure:

1.) N [R/S] display X [X<>Y] Y continue [R/S] if it is more than one solution and continue until steps 2.) shown mean finish.

2.) N [R/S] display 0.000000000 then 0.00 indicate that "No Solution"

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Example:

X^2 + Y^2 = 41

N = 41

41 [R/S] 4 [X<>Y] 5 [R/S] "0.000000000" 0.00

Answer: X = 4 and Y = 5
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X^2 + Y^2 = 76789

N = 76789

76789 [R/S] 135 [X<>Y] 242
[R/S] 150 [X<>Y] 233
[R/S] "0.000000000" 0.00

Answer:
X = 135 and Y = 242
X = 150 and Y = 233
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Program:

Code:

 
01 STO 3
02 √X
03 INTG
04 STO 0
05 RCL 3
06  2
07  ÷
08 √X
09 STO 1
10 RCL 0
11 RCL 1
12 X≤Y
13 GTO 23
14 RCL 1
15 FRAC
16 X=0
17 GTO 10
18 CLx
19 FIX 9
20 PSE
21 FIX 2
22 GTO 00
23 RCL 3
24 RCL 0
25 ENTER
26  x
27  -
28 √X
29 ENTER
30 INTG
31 X<>Y
32 X≤Y
33 GTO 39
34 RCL 0
35  1
36  -
37 STO 0
38 GTO 10
39 RCL 0
40 X<>Y
41 R/S
42 GTO 34

Remark: Try this on 12C Emulator: N = 9876543210

Gamo