# HP Forums

Full Version: (11C) Sums of Three Squares
You're currently viewing a stripped down version of our content. View the full version with proper formatting.
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"

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

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

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

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
Reference URL's
• HP Forums: https://www.hpmuseum.org/forum/index.php
• :