Instructive FE (I desperately need that topic list)

For discussing Olympiad Level Algebra (and Inequality) problems
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Zawadx
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Joined:Fri Dec 28, 2012 8:35 pm
Instructive FE (I desperately need that topic list)

Unread post by Zawadx » Wed Feb 15, 2017 9:32 pm

$ f: \mathbb{N} \rightarrow \mathbb{N} $
$f(n) + f(f(n)) = 6n $

Find $ f(n)$

rah4927
Posts:110
Joined:Sat Feb 07, 2015 9:47 pm

Re: Instructive FE (I desperately need that topic list)

Unread post by rah4927 » Sun Feb 19, 2017 11:23 am

Some hints.

First try to guess the answer. Done? Let's move on.

Now there aren't a lot of things you can do in this problem apart from proving $f$ is injective, and even that doesn't yield much. So you can only plug in values. Plug in $n=1$. First assume that $f(1)=1$. Keep reiterating the values to see what happens. Does it become negative at some point? If so, try with more values and see if something becomes negative.

Finally, try to prove this.

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