2

Part of 2004 Baltic Way

Problems(1)

P(1/x) * P(x) >= 1 for x = 1 ==> also for every x > 0

Source: Arthur Engel, intended German TST problem 2004; Baltic Way 2004, problem 2

P(x)

be a polynomial with a non-negative coefficients. Prove that if the inequality

P\left(\frac {1}{x}\right)P(x)\geq 1

holds for x \equal{} 1, then this inequality holds for each positive

x

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