21P(x)^2 = P(-x)^2
P(x) = P(-x)
or P(x)+ P(-x) = 0
If P(x) + P(-x) = 0
P(0) = 0
P(1) = 1
P(2) = P(1)^2 + 1= 2
P(5) = P(2)^2 + 1= 5
There may exists lot of solutions,can u give us the source?
Find all functions p:\mathbb{Z}\Rightarrow\mathbb{Z} such that p(x^2+1)=p(x)^2+1.
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4 Answers
21
21I got only 2 solutions during the test P(x)=x and P(x)=|x|
Here goes Prophet sir's solution:http://www.goiit.com/posts/list/algebra-sir-please-reply-me-72058.htm#354976
and PCO's solution: http://www.artofproblemsolving.com/Forum/viewtopic.php?f=57&t=446051&p=2510734#p2510734
