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Prove the degree of f(x) is at least n.

Source: Hungary-Israel Mathematical Competition 2007 Problem 6

November 19, 2007
algebrapolynomialalgebra unsolved

Problem Statement

Let t≥3 t \ge 3 be a given real number and assume that the polynomial f(x) f(x) satisfies |f(k)\minus{}t^k|<1, for k\equal{}0,1,2,\ldots ,n. Prove that the degree of f(x)f(x) is at least nn.
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