What is the general form of a polynomial p(x) such that that$$ p(x^2)=p(x)^2$$

Question

anonymous · Answer

x^n

anonymous · Answer

Darn, I went to take a drink of OJ and Avinash wrote it first.

anonymous · Answer

$$f(x)=x$$

anonymous · Answer

lol ok i l make up for that

anonymous · Answer

You're too nice, Avinash! :)

anonymous · Answer

thanks i guess :)

anonymous · Answer

or rather $$\left( f(x)\right) ^n=x^n$$

anonymous · Answer

x^n

anonymous · Answer

@eliassaab
how do we can prove that only root of polynomial is 0?

anonymous · Answer

Apart from 0 complex numbers with |a| = 1 are only possible roots but i cant cancel them.
it seems easier than the other problems but i dony know...

anonymous · Answer

i think its trivial because there r infinite complex numbers with |a| = 1 and if one of them is root then the others must be too and this is not true because a polynomial can only have a finite number of roots

anonymous · Answer

@eliassaab
thank u sir
for the nice problems u put up