IMO 1993(1)

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SANZEED
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IMO 1993(1)

Unread post by SANZEED » Fri Jun 01, 2012 12:57 am

Let $n>1$ be an integer and let $f(x)=x^{n}+5x^{n-1}+3$. Prove that there do not exist polynomials $g(x),h(x)$ each having integer coefficients and degree at least one such that $f(x)=g(x)h(x)$.
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SANZEED
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Re: IMO 1993(1)

Unread post by SANZEED » Fri Jun 01, 2012 1:03 am

I would have never dared to read the 1st section of IMO compendium. But when I found this problem ,I searched about the polynomials in it and came to know about Eisenstein's criterion (extended),which just kills the problem! :shock: 8-) 8-)
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Phlembac Adib Hasan
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Re: IMO 1993(1)

Unread post by Phlembac Adib Hasan » Fri Jun 01, 2012 4:19 pm

SANZEED wrote:
I would have never dared to read the 1st section of IMO compendium. But when I found this problem ,I searched about the polynomials in it and came to know about Eisenstein's criterion (extended),which just kills the problem! :shock: 8-) 8-)
You can also find it in Elementary Number Theory.(with proof)
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