(41C) Sum of Two Squares
08-17-2019, 01:38 PM
Post: #1 Eddie W. Shore Senior Member Posts: 1,075 Joined: Dec 2013
(41C) Sum of Two Squares
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