I am a student and gave my 10 grade exam last month. I am preparing for Mathematics Olympiads. I saw some questions regarding finding polynomials that satisfy some equation or condition. For e.g.
Find all polynomials such that $P(x^2+1)=P(x)^2+1$
I am looking for some book that would be available online in pdf format that shows how to solve such problems from very basic that I can understand. I have never solved such problems. I have looked on some solutions but I am not able to understand them.
Thanks in advance!