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Let a_1,a_2,\ldots a_n,k, and M be positive integers such that \frac{1}{a_1}+\frac{1}{a_2}+\cdots+\frac{1}{a_n}=k\quad\text{and}\quad a_1a_2\cdots a_n=M.If M>1, prove that the polynomial P(x)=M(x+1)^k-(x+a_1)(x+a_2)\cdots (x+a_n)has no positive roots.

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