This problem maybe quite easy but I've not solved it yet.
Let $n$ be a positive integer. Show that the numbers
\[\binom{2^n-1}{0},\binom{2^n-1}{1},\binom{2^n-1}{2},\cdot \cdot \cdot ,\binom{2^n-1}{2^{n-1}-1}\]
are congruent modulo $2^{n}$ to $1,3,5,\cdot \cdot \cdot ,2^{n}-1$ in some order.
Turzo
IMO SL N4(2008)
- Sazid Akhter Turzo
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Last edited by Sazid Akhter Turzo on Tue Apr 03, 2012 8:55 pm, edited 1 time in total.
- Phlembac Adib Hasan
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Re: IMO SL N4(2008)
Not realizing the last line.Better if you give an example.
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- Sazid Akhter Turzo
- Posts:69
- Joined:Sat Feb 18, 2012 9:15 am
- Location:Sirajganj
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Re: IMO SL N4(2008)
Oh-ho!!! I made serious mistake . It's actually $2^{n}$, not $2$. I've just edited it.
Turzo
Turzo