IMO 2012: Day 2 Problem 6

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Moon
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IMO 2012: Day 2 Problem 6

Unread post by Moon » Thu Jul 12, 2012 1:19 am

Find all positive integers $n$ for which there exist non-negative integers $a_1,a_2,\cdots, a_n$ such that \[\frac{1}{2^{a_1}}+\frac{1}{2^{a_2}}+\cdots+\frac{1}{2^{a_n}}=\frac{1}{3^{a_1}}+\frac{2}{3^{a_2}}+\cdots+\frac{n}{3^{a_n}}=1\]
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Masum
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Re: IMO 2012: Day 2 Problem 6

Unread post by Masum » Thu Jul 12, 2012 1:24 am

অনেক দিন পরে ৬ এ ক্ল্যাসিক নাম্বার থিওরি দেখলাম। :)
One one thing is neutral in the universe, that is $0$.

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