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 2011-06-13, 14:44 #1 JohnFullspeed   May 2011 France 7·23 Posts Magic squaress Sometimes you can write a value like the sum of two square i/e 16+25= 51.... a= b²+c² Are b and c unics? John
2011-06-13, 14:53   #2
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by JohnFullspeed Sometimes you can write a value like the sum of two square i/e 16+25= 51.... a= b²+c² Are b and c unics? John
What is a "unic"? I presume that you do not mean Eunuch.

It is a fairly simple elementary exercize to determine when a number
is the sum of two squares. It is an exercize for a 1st year number theory
class to determine when the representation is unique.

May I suggest that you perform some numerical experimentation to see
if you can hypothesize when the representation is unique.

2011-06-13, 14:58   #3
Mr. P-1

Jun 2003

22218 Posts

Quote:
 Originally Posted by JohnFullspeed Sometimes you can write a value like the sum of two square i/e 16+25= 51.... a= b²+c² Are b and c unics? John
No. For example: 5²+10² = 11²+2²

2011-06-13, 15:03   #4
R.D. Silverman

Nov 2003

22×5×373 Posts

Quote:
 Originally Posted by Mr. P-1 No. For example: 5²+10² = 11²+2²
Don't spoil it!!!!!!

 2011-06-13, 15:24 #5 davieddy     "Lucan" Dec 2006 England 11001010010102 Posts "Magic Squaress" sound's like the ideal title to bestow on Alice Through the Looking Glass Last fiddled with by davieddy on 2011-06-13 at 15:32
2011-06-13, 16:08   #6
Ralf Recker

Oct 2010

191 Posts

Quote:
 Originally Posted by JohnFullspeed Sometimes you can write a value like the sum of two square i/e 16+25= 51.... a= b²+c² Are b and c unics? John
51?

Last fiddled with by Ralf Recker on 2011-06-13 at 16:09

2011-06-13, 16:36   #7
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

100000110000002 Posts

Quote:
 Originally Posted by Ralf Recker 51?
my guess is they either don't know math or that's a typo as 4 is next to 5 on the keyboard and the answer really is 41 in decimal.

 2011-06-13, 18:01 #8 JohnFullspeed   May 2011 France 101000012 Posts Sorry http://www.mersenneforum.org/showthread.php?t=15623 In fact i need to find 5 polynoms a²+b²+c²+d².....i²+j² =Z Is there a math mehod? thanks Last fiddled with by JohnFullspeed on 2011-06-13 at 18:16 Reason: typo errors
2011-06-13, 18:32   #9
R.D. Silverman

Nov 2003

22·5·373 Posts

Quote:
 Originally Posted by JohnFullspeed http://www.mersenneforum.org/showthread.php?t=15623 In fact i need to find 5 polynoms a²+b²+c²+d².....i²+j² =Z Is there a math mehod? thanks
As posted, this is gibberish. No problem is presented. No question
is asked. What are you looking for? 5 polynomials for what?
You have only defined an integer Z as the sum of 10 squares.

Last fiddled with by R.D. Silverman on 2011-06-13 at 18:36

2011-06-13, 19:05   #10
science_man_88

"Forget I exist"
Jul 2009
Dumbassville

26·131 Posts

Quote:
 Originally Posted by R.D. Silverman As posted, this is gibberish. No problem is presented. No question is asked. What are you looking for? 5 polynomials for what? You have only defined an integer Z as the sum of 10 squares.
magic squares wouldn't ever have 10 squares either as they are n by n with a magic constant so I can't so far make any sense of it either.

2011-06-13, 19:06   #11
CRGreathouse

Aug 2006

135118 Posts

Quote:
 Originally Posted by R.D. Silverman You have only defined an integer Z as the sum of 10 squares.
...which doesn't even tell us anything about Z, since all nonnegative integers are the sum of 10 squares.

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