Write a full solution.
Let be real polynomials (real coefficients) with leading coefficient or such that , find the number of solutions to . If possible, find each forms of solution.
Let . Find all possible values of where is a positive integer. (Where is a floor function, and defined to be )
Find all real polynomials that satisfy for all reals that satisfy .
This note is part of Thailand Math POSN 3rd round 2015