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Is the set of polynomials $a_0+a_1x+\ldots+a_nx^n$, where $2^{k+1}$ divides $a_k$, an ideal in $\mathbb{Z}[x]$? How should I think about this?

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What happens under multiplication with $x$? – martini Nov 8 '12 at 6:57
@martini: nice hint, thanks. – Carolus Nov 8 '12 at 7:26
up vote 3 down vote accepted

Can you se what happens when you multiply an element of that set by a polynomial; by $x$ for example?

Another approach, your set contains the constant $2$; if it were an ideal, it should contain all polynomials divisible by $2$. Does it?

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I get it, thanks! – Carolus Nov 8 '12 at 7:28

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