Find the polynomials

Asked Dec 10 '19 at 01:30

Active Dec 10 '19 at 01:30

Viewed 32 times

Find all polynomial $P$ satisfying $P(x^2+1)=P(x)^2+1$

Attemp: I haven't proved it, but i suspect that this are all of them: $p(x) \equiv \frac{1+i\sqrt{3}}{2}$

$p(x) \equiv \frac{1-i\sqrt{3}}{2}$

and all the iterations of $x^2+1$:

$p(x)=x$

$p(x)=x^2+1$

$p(x)=(x^2+1)^2+1$

$p(x) = ((x^2+1)^2+1)^2+1$ :

asked Dec 10 '19 at 01:30

Sullo

This is an old problem. Probably it is also in this website. – topeik Dec 10 '19 at 01:36
Ah, yes. Here they have it too. – topeik Dec 10 '19 at 01:39
@topeik Is your name Lucas? – Sullo Dec 10 '19 at 01:44
@Sullo I wish. My name makes no sense. – topeik Dec 10 '19 at 01:45
@topeik How can I communicate with you? – Sullo Dec 10 '19 at 01:50
You are already. – topeik Dec 10 '19 at 01:52

0 Answers0