(12C) Sums of Two Squares
01-06-2019, 05:07 AM (This post was last modified: 01-06-2019 05:29 AM by Gamo.)
Post: #1 Gamo Senior Member Posts: 597 Joined: Dec 2016
(12C) Sums of Two Squares
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

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
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