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For a positive integer n, let

 

                                                                            \(R_n = \underbrace{111 \dots 1}_{n \text{ 1s}}.\)

                                                            
For example, \(R_4 = 1111.\)

Find the polynomial p(x) such that \(p(R_n) = R_{2n + 1}\) for all positive integers n. (Give your answer in base 10.)

 Jun 6, 2020
 #1
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The polynomial is p(x) = 9x^2 - 10x + 1.

 Oct 5, 2020

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