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).
+605 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.
