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+--- Thread: (11C) Sums of Three Squares (/thread-12128.html)
(11C) Sums of Three Squares - Gamo - 01-07-2019 12:09 PM
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
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 4Gamo
RE: (11C) Sums of Three Squares - Albert Chan - 01-07-2019 05:06 PM
(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