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Let p(x) be a monic polynomial of degree 6 such that p(2^n) = n for n = 0, 1, 2, ..., 6.  Find p(0).

 Feb 22, 2021
 #1
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I will avoid using the Lagrange Interpolation Formula here because it is insanely overkill.

 

Using the method of undetermined coefficients the answer is $\boxed{1}$.

 

Another way is to look at finite differences and take the last number.

 Feb 23, 2021

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