Poly polynomials

Level pending

Let $P_1(x) = x^2 - 2$ and $P_i(x) = P_1 (P_{i-1}(x))$ for $i \geq 2$ . Let $N$ denote the number of real roots of $P_{2014}(x)$ . Find the first three digits of $\log_2{N}$ .

Details and assumptions

Each root is counted once, regardless of it's multiplicity.

The answer is 201.

1 solution

A Brilliant Member
Jan 8, 2014

This problem is not original. I give full credit to IMO 1976 for this beautiful problem. Hint: put $x=2 \cos{\theta}$ . For full solution, you may refer IMO 1976.

This problem was rather easy, but note that you are accepting the wrong answer.

Firstly, I'm not sure if there is any way to compute the first three digits of $2^{2014}$ without using a calculator. Secondly, the first three digits of $2^{2014}$ are $188$ , not $201$ .

Sreejato Bhattacharya - 7 years, 5 months ago

I corrected the question... Thanks Sreejato.

A Brilliant Member - 7 years, 5 months ago

nice question bro ! (y)

Rohan Chandra - 7 years, 5 months ago

Poly polynomials

The answer is 201.

1 solution

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