Problem

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Tags: induction, algebra proposed, algebra



Let $ a_{0},a_{1},\ldots,a_{n}$ be integers, one of which is nonzero, and all of the numbers are not less than $ - 1$. Prove that if \[ a_{0} + 2a_{1} + 2^{2}a_{2} + \cdots + 2^{n}a_{n} = 0,\] then $ a_{0} + a_{1} + \cdots + a_{n} > 0$.