Functional Eqution

VITEEE 2015 Tutorials › Olympiad Stuff questions › Functional Eqution

Find all functions p:\mathbb{Z}\Rightarrow\mathbb{Z} such that p(x^2+1)=p(x)^2+1.

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Shubhodip ·2011-11-16 11:14:05

P(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?

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Arnab Kundu ·2011-11-16 20:18:07

The source is Ramanujan School of Mathematics RMO Practice test

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Arnab Kundu ·2011-11-16 20:21:30

I 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

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Aditya Bhutra ·2011-11-16 23:33:31

p(x)=[x] will also be one of the solns.

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° ∂ ∞ α β γ δ θ λ μ ν ξ π ρ σ φ ω ε ƒ κ τ υ Γ Δ Λ Σ Π Ω

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Functional Eqution

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