IMO Preparation Mock 1 Problem 3

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zadid xcalibured
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IMO Preparation Mock 1 Problem 3

Unread post by zadid xcalibured » Mon Apr 15, 2013 7:59 pm

Find all positive integers $m,n \geq 2$,such that,
$1$. $m+1$ is a prime number of the form $4k-1$
$2$.there is a prime number $p$ and non-negative integer $a$,such that
\[\frac{m^{2^{n}-1}-1}{m-1}=m^{n}+p^{a}\]

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Phlembac Adib Hasan
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Re: IMO Preparation Mock 1 Problem 3

Unread post by Phlembac Adib Hasan » Tue Apr 16, 2013 2:10 pm

China TST 2010 Quiz 1 Problem 3.
$n$ even-এর কেসটা সোজা, mod $p^2$ নিলেই কাজ শেষ। একটাই সল্যু. আসে $n=2,a=1,m=p-1$. $n$ odd-এর কেসটা কঠিন। Trying...
@ জাদিদ ভাই, এইটা করসেন? করলে সল্যু. পোস্ট দেন।

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zadid xcalibured
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Re: IMO Preparation Mock 1 Problem 3

Unread post by zadid xcalibured » Tue Apr 16, 2013 10:08 pm

না ভাই।করি নাই।করার চেষ্টা করতেছি।করলে দিব সল্যুশান। :mrgreen:

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