LOGIN/REGISTER
Please Wait...
It is currently Sep 02, 2010, 11:31 am
Post new topic Reply to topic  Page 1 of 1
  [ 5 posts ]  Share: Facebook
Author Message
makar
Riemann Hypothesis
User avatar

Posts: 277
Location: India
India
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) .
 
 
Brut3Forc3
Birch & Swinnerton Dyer
User avatar

Posts: 2960
Location: Irvine, CA
China    United States
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
 
 
makar
Riemann Hypothesis
User avatar

Posts: 277
Location: India
India
Post Posted: Sep 13, 2009, 11:31 pm • # 3 


Is there any general solution for it
 
 
vijaymenon
Yang-Mills Theory
User avatar

Posts: 599
Location: Chennai
India
Post Posted: Sep 13, 2009, 11:41 pm • # 4 


Good solution :P
 
 
makar
Riemann Hypothesis
User avatar

Posts: 277
Location: India
India
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  
  Share on Facebook Previous topic | Next topic 

Community » Olympiad Section » Algebra » Algebra Unsolved Problems

All times are UTC - 8 hours [ DST ]
Share: Facebook

Moderator: High School Olympiad Moderators

Post new topic Reply to topic  Page 1 of 1
  [ 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

Intermediate Algebra
A complete Algebra II course, with many Precalculus topics. Over 1000 problems! Great for AMC and AIME preparation.
Intermediate Counting & Probability
The sequel to Introduction to Counting & Probability. Over 650 problems! Great for AMC and AIME preparation.