## AN INTERESTING PROBLEM BY SAKAL DA

For discussing Olympiad Level Algebra (and Inequality) problems
MATHPRITOM
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### AN INTERESTING PROBLEM BY SAKAL DA

${a_0}=2,$

${a_n}=2012+{a_0}{a_1}{a_2}{a_3}...{a_{n-2}}{a_{n-1}}$ .

Find out ${a_{2012}}$.

SANZEED
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Joined: Wed Dec 28, 2011 6:45 pm

### Re: AN INTERESTING PROBLEM BY SAKAL DA

$a_{2012}=2012+2^{2^{2011}}$
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

MATHPRITOM
Posts: 190
Joined: Sat Apr 23, 2011 8:55 am
Location: Khulna

### Re: AN INTERESTING PROBLEM BY SAKAL DA

Hi,little brother ,plz, give the full solution.

SANZEED
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Joined: Wed Dec 28, 2011 6:45 pm

### Re: AN INTERESTING PROBLEM BY SAKAL DA

upssssss........sorrry..........got the mistake probably
$\color{blue}{\textit{To}} \color{red}{\textit{ problems }} \color{blue}{\textit{I am encountering with-}} \color{green}{\textit{AVADA KEDAVRA!}}$

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### Re: AN INTERESTING PROBLEM BY SAKAL DA

Let $b_n=a_n-2012$ notice that $a_n$ depends totally on $a_{n-1}$.$a_{n-1}-2012=a_n(a_n-2012)$
So $b_{n+1}=b_n(b_n+2012)$
Then the general formula can be established using induction.I see no better way right now.

asif e elahi
Posts: 183
Joined: Mon Aug 05, 2013 12:36 pm
zadid xcalibured wrote:Let $b_n=a_n-2012$ notice that $a_n$ depends totally on $a_{n-1}$.$a_{n-1}-2012=a_n(a_n-2012)$
So $b_{n+1}=b_n(b_n+2012)$