2020 CAMO Problems/Problem 5

Revision as of 14:21, 5 September 2020 by Jbala (talk | contribs) (Created page with "==Problem 5== Let <math>f(x)=x^2-2</math>. Prove that for all positive integers <math>n</math>, the polynomial <cmath>P(x)=\underbrace{f(f(\ldots f}_{n\text{ times}}(x)\ldots)...")
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Problem 5

Let $f(x)=x^2-2$. Prove that for all positive integers $n$, the polynomial \[P(x)=\underbrace{f(f(\ldots f}_{n\text{ times}}(x)\ldots))-x\]can be factored into two polynomials with integer coefficients and equal degree.

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See also

2020 CAMO (ProblemsResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6
All CAMO Problems and Solutions
2020 CJMO (ProblemsResources)
Preceded by
Problem 5
Followed by
Last problem
1 2 3 4 5 6
All CJMO Problems and Solutions

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