Largest prime number (1 Viewer)

juantheron · Jul 13, 2017

$Finding largest prime number which divide $\displaystyle \binom{2000}{1000}$

$We can write $\displaystyle \binom{2000}{1000} = \frac{2000!}{1000!\cdot 1000!} = \frac{1001 \cdot 1002 \cdot 1003\cdots \cdots 2000}{1000!}$

i did not understand how to solve further, please explain me

dan964 · Jul 13, 2017

juantheron said:
$Finding largest prime number which divide $\displaystyle \binom{2000}{1000}$

$We can write $\displaystyle \binom{2000}{1000} = \frac{2000!}{1000!\cdot 1000!} = \frac{1001 \cdot 1002 \cdot 1003\cdots \cdots 2000}{1000!}$

i did not understand how to solve further, please explain me

You can simplify further to
$\noindent \frac{1001 \cdot 2 \cdot 1003 \cdot 2 \cdots 1999 \cdot 2}{500!} \\ $ $ \\ =\frac{2002 \cdot 2006 \cdots 3998}{500!} \\ $ $ \\ =\frac{1001 \cdots 1999}{250! \cdot 3 \cdot \cdots 499}$

Largest prime number (1 Viewer)

juantheron

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dan964

what

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