(11C) Sums of Three Squares

[Gamo]

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

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

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

where X ≤ Y ≤ Z

-------------------------------------------------------------------

Procedure:

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

2.) N [A] display 0.000000000 then 0.00 indicate that "No Solution"

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Example:

X^2 + Y^2 + Z^2 = 9876543210

9876543210 [A] display 99380 [Rv] 391 [Rv] 77

[R/S] 99380 [Rv] 359 [Rv] 173

[R/S] "0.000000000" 0.00

Answer:

X=77 Y=391 Z=99380
X=173 Y=359 Z=99380
----------------------------------------------------
Program:

Code:


LBL A
STO 4
√X
INT
STO 1
RCL 4
3
÷
√X
STO 2
RCL 4
RCL 1
X^2
-
STO 3
2
÷
√X
STO 5
RCL 3
√X
INT
STO 0
-------------------------
LBL 1
RCL 1
RCL 2
X≤Y
GTO 2
CLx
FIX 9
PSE
FIX 4
RTN
------------------------
LBL 2
RCL 0
RCL 5
X≤Y
GTO 3
RCL 1
1
-
STO 1
GTO 1
---------------------
LBL 3
RCL 3
RCL 0
X^2
-
√X
ENTER
INT
X=Y
GTO 5
-------------------
LBL 4
RCL 0
1
-
STO 0
GTO 2
------------------
LBL 5
RCL 0
RCL 1
R/S
GTO 4

Gamo

[Albert Chan]

(01-07-2019 12:09 PM)Gamo Wrote:  Example:

X^2 + Y^2 + Z^2 = 9876543210

Answer:

X=77 Y=391 Z=99380
X=173 Y=359 Z=99380

there are many, many more !

X=388 Y=455 Z=99379
X=541 Y=680 Z=99377
X=553 Y=805 Z=99376
X=100 Y=1241 Z=99373
X=385 Y=1184 Z=99373
X=351 Y=1275 Z=99372
X=145 Y=1388 Z=99371
X=313 Y=1360 Z=99371
X=400 Y=1337 Z=99371
X=812 Y=1135 Z=99371
...

It might be better to test smaller number, say Year 2019.

2019
= 1² + 13² + 43²
= 5² + 25² + 37²
= 7² + 11² + 43²
= 7² + 17² + 41²
= 11² + 23² + 37²
= 13² + 13² + 41²
= 13² + 25² + 35²
= 17² + 19² + 37²
= 23² + 23² + 31²