# Easy Polynomo!

Let $$n$$ be a positive integer and $$P(x)$$ a polynomial of degree $$2n$$ such that $$P(0) = 1$$ and $$P(k) = 2^{k-1}$$ for $$k=1,2,3, \ldots, 2n$$.

Prove that $$2P(2n+1) - P(2n+2)=1$$.

Note by Satyajit Mohanty
1 year, 12 months ago

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I found a proof with method of differences. Interesting how one can consider part of the chart to be a function following f(n)=2^n for n in domain, but then have an extra column with alternating 1s and 0s. My latex is bad. I hope you see where I am going.

- 1 year, 11 months ago