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Let P(x) be a polynomial of degree 2m. Show that \( P(x^2)= P(x)P(x-1) \) if and only if \[ P(x) =\left( x^2 + x+1 \right)^m\]
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See http://openstudy.com/study#/updates/4ff6b092e4b01c7be8c98dee for the particular case where m=5.
hmm looks like all the heavy lifting was done showing that since the only roots are \(-\frac{1}{2}\pm\frac{\sqrt{3}}{2}i\) it must be \((x^2+x+1)^m\) is that the hook, or is there something else?
I agree. I posted so people can see that it is true in this general form.
ok then kudos to @mukushla who did all the work for this one
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