IMO Shortlist 2007 N1

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Phlembac Adib Hasan
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IMO Shortlist 2007 N1

Unread post by Phlembac Adib Hasan » Thu Jan 03, 2013 10:09 am

Find all pairs $(k,n)$ of positive integers for which $7^k-3^n|k^4+n^2$.
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Phlembac Adib Hasan
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Re: IMO Shortlist 2007 N1

Unread post by Phlembac Adib Hasan » Thu Jan 03, 2013 10:14 am

My steps:
At first prove $k,n$ even. Then prove for 'sufficiently large' $k,n$,
$7^{k/2}>k^4;\; \; 3^{n/2}>n^2$
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zadid xcalibured
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Re: IMO Shortlist 2007 N1

Unread post by zadid xcalibured » Thu Jan 03, 2013 2:44 pm

My steps:
Adib's steps. :mrgreen:
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