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a) Find all polynomials $p(x)$ such that $p(q(x)) = q(p(x))$ for every polynomial $q(x)$.

b) Find all polynomials $p(x), q(x)$ such that $p(q(x)) = q(p(x))$.

Thanks

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    Yes,I have.I have made as far as the answers were given.But wasnt able to proof if more than the solutions i have provided exist!2012-10-16

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HINT: Consider what happens if $q(x)$ is a constant polynomial, say $q(x)=a$: $p(a)=p\big(q(x)\big)=q\big(p(x)\big)=a\;.$

But there’s a constant polynomial for every $a\in\Bbb R$, so ... ?

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    @Sai: You’re welcome.2012-10-16