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Post Posted: May 04, 2007, 11:46 pm • # 1 


For each function f which is defined for all real numbers and satisfies

f(xy)=xf(y)+yf(x)

and

f(x+y)=f(x^{1993})+f(y^{1993})

determine the value f(\sqrt{5753}).
 
 
Post Posted: May 05, 2007, 9:27 am • # 2 


BanishedTraitor wrote:
For each function f which is defined for all real numbers and satisfies

f(xy)=xf(y)+yf(x)

and

f(x+y)=f(x^{1993})+f(y^{1993})

determine the value f(\sqrt{5753}).


Maybe a bit of progress...

_________________
Say this ten times quickly: The product of the sums of squares is greater than the square of the sum of products!
 
 
Post Posted: May 05, 2007, 9:29 am • # 3 


Good start ... you might try Hidden Text

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Joel
Hi Deeps! <3
 
 
Post Posted: May 05, 2007, 9:40 am • # 4 


JBL wrote:
Good start ... you might try Hidden Text


Alright,

_________________
Say this ten times quickly: The product of the sums of squares is greater than the square of the sum of products!
 
 
Post Posted: May 05, 2007, 4:14 pm • # 5 


root 5753 is not in Z

_________________
-Alex
Altheman's Problem Column
 
 
Post Posted: May 05, 2007, 4:17 pm • # 6 


The last step
Question: What family of functions is described by the first condition alone?

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Annoying Precision (http://qchu.wordpress.com/)
 
 
Post Posted: May 06, 2007, 7:41 am • # 7 


Altheman wrote:
root 5753 is not in Z


Yea, sorry, but I was working from what I had in my first post. :P

_________________
Say this ten times quickly: The product of the sums of squares is greater than the square of the sum of products!
 
 
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