APMO 1998-5

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SANZEED
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APMO 1998-5

Unread post by SANZEED » Sun Jun 03, 2012 2:32 am

Determine the largest of all integers $n$ with the property that $n$ is divisible by all natural numbers $\leq \sqrt[3]{n}$
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Re: APMO 1998-5

Unread post by Phlembac Adib Hasan » Sun Jun 03, 2012 6:57 am

Bartrand's postulate can help here.
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SANZEED
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Re: APMO 1998-5

Unread post by SANZEED » Sun Jun 03, 2012 11:08 am

Will you please assert the Postulate named as "Bartrand's postulate"?
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Re: APMO 1998-5

Unread post by Phlembac Adib Hasan » Sun Jun 03, 2012 5:43 pm

SANZEED wrote:Will you please assert the Postulate named as "Bartrand's postulate"?
For $n>1$, there is a prime between $n$ and $2n$.
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Re: APMO 1998-5

Unread post by Masum » Sat Oct 27, 2012 12:40 am

Let's say you don't know Bertrand's Postulate, nor its proof. How will solve it then? It has at least one fully elementary solution. :)
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