Let $P(x)=x^{n}+a_{n-1}x^{n-1}+ \ldots +a_1x+1$ with integer coefficients Prove that there exist infinitely $x, y \in \mathbb{N^*}$ such that $y | P(x)$ and $x|P(y)$
Sorry because I don't write what I've done
Please give me some hints
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1What does $P(x) \vdots y$ mean? – Daniel Fischer Dec 05 '13 at 12:34
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mean P(x) is divisible by y – tangkhaihanh Dec 05 '13 at 12:42
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1Ah. Where I come from, that's usually written $y \mid P(x)$, $y$ divides $P(x)$. – Daniel Fischer Dec 05 '13 at 12:47
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And we use both :) – tangkhaihanh Dec 05 '13 at 12:52
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At the cost of having to explain the less common notation sometimes ;) – Daniel Fischer Dec 05 '13 at 12:54
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ok,I've just edited – tangkhaihanh Dec 05 '13 at 13:00