(41C) Sum of Two Squares

[Eddie W. Shore]

Given a positive integer n, can we find two non-negative integers x and y such that:

n = x^2 + y^2

(x and y can be 0, n is assumed to be greater than 0)

The program presented here is the use of iterations to find all possible pairs which fit n = x^2 + y^2. Some integers do not have representations, others have more than one. The program will show all possible combinations.

Registers used:
R00 = n
R01 = counter
R02 = temporary

Code:


01 LBL T^SUMSQRS
02 FIX 0
03 STO 00
04  2
05  /
06  SQRT
07  INT
08  1000
09  /
10  STO 01
11  LBL 00
12  RCL 00
13  RCL 01
14  INT
15  X↑2
16  -
17  SQRT
18  STO 02
19  FRC
20  X=0?
21  GTO 01
22 GTO 02
23 LBL 01
24 RCL 01
25 INT
26 T^X = 
27 ARCL X
28  AVIEW
29  STOP
30  RCL 02
31  T^Y = 
32 ARCL X
33 AVIEW
34 STOP
35 LBL 02
36  ISG 01
37  GTO 00
38  T^END
39  VIEW
40  FIX 4
41  RTN

Examples

Example 1: n = 325
325 = 1^2 + 18^2
325 = 6^2 + 17^2
325 = 10^2 + 15^2

Example 2: n = 530
530 = 1^2 + 23^2
530 = 13^2 + 19^2

Blog link: http://edspi31415.blogspot.com/2019/08/h...f-two.html