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Inequality in three variables and product.

Source: Vietnam MO 1982 P5

March 17, 2011
inequalitiesinequalities unsolved

Problem Statement

Let pp be a positive integer and q,zq, z be real numbers with 0\le q\le 1 and q^{p+1}\le z\le 1. Prove that ∏k=1p∣z−qkz+qk∣≤∏k=1p∣1−qk1+qk∣.\prod_{k=1}^p \left|\frac{z - q^k}{z + q^k}\right| \le\prod_{k=1}^p \left|\frac{1 - q^k}{1 + q^k}\right|.
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