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(n^3+3n)^2/(n^6-64)

Source: IMC 2019 Day 1 P1

July 31, 2019
college contests

Problem Statement

Evaluate the product ∏n=3∞(n3+3n)2n6−64.\prod_{n=3}^{\infty} \frac{(n^3+3n)^2}{n^6-64}.
Proposed by Orif Ibrogimov, ETH Zurich and National University of Uzbekistan and Karen Keryan, Yerevan State University and American University of Armenia, Yerevan
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