Understand the problem
Source of the problem
Start with hints
As is divisible by , there exists a polynomial such that . Let be a zero of . If then , i.e. . The given equation means that are also zeroes of . Claim One of the two numbers is greater than 1. Proof Suppose that they are both . Then we have Adding these two inequalities we get which is absurd. Hence at least one of them has to be greater than 1. The claim means that, if is non-zero, then at least one of the two zeroes has absolute value greater than .
Now let , the zero of with the largest absolute value. The procedure mentioned above can be used to construct a zero with absolute value bigger than , which is absurd unless . As is largest among the zeroes in absolute value, this means that does not have any nontrivial zeroes. Hence for some and .
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