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+--- Thread: (41C) Sum of Two Squares (/thread-13469.html)
(41C) Sum of Two Squares - Eddie W. Shore - 08-17-2019 01:38 PM
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 RTNExamples
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/hp-prime-and-hp-41cdm-41l-sum-of-two.html