I have a problem that I can't solve.You can help me!

On the blackboard,the mathematics professor wrote a poly monial f(x) with interger coefficient and said,"Today is my son's birthday.When his age A is substitute for x,f(A)=A.You will note also that f(0)=P and that P is a prime number geater than A".How old is the professor's son?

Thaks for advance for your solution!

Thank you so much!!!