LOGIN/REGISTER
Please Wait...
It is currently Sep 02, 2010, 11:31 am
Post new topic Reply to topic  [ 5 posts ]  Share: Facebook
Message
Post Posted: Sep 13, 2009, 3:13 pm • # 1 


Let X be the set of all positive integers greater than or equal to 8 and let f: X\rightarrow X be a function such that f(x+y)=f(xy) for all x\ge 4, y\ge 4 . if f(8)=9, determine f(9) .
 
 
Post Posted: Sep 13, 2009, 4:24 pm • # 2 


We have f(8)=f(4+4)=f(16)=f(8+8)\\=f(64)=f(16+4)=f(20)=f(5+4)=f(9).

_________________
"I can stand brute force, but brute reason is quite unbearable. There is something unfair about its use. It is hitting below the intellect." - Oscar Wilde
 
 
Post Posted: Sep 13, 2009, 11:31 pm • # 3 


Is there any general solution for it
 
 
Post Posted: Sep 13, 2009, 11:41 pm • # 4 


Good solution :P
 
 
Post Posted: Sep 14, 2009, 12:59 am • # 5 


http://www.artofproblemsolving.com/viewtopic.php?s ... 7&t=247690
 
 
Display posts from previous:  Sort by  

All times are UTC - 8 hours [ DST ]

Share: Facebook

Moderator: High School Olympiad Moderators

Post new topic Reply to topic  [ 5 posts ] 

Login

Username:   Password:   Log me on automatically each visit  

You cannot post new topics in this forum
You cannot reply to topics in this forum
You cannot edit your posts in this forum
You cannot delete your posts in this forum
You cannot post attachments in this forum