International Mathematics Competition
for University Students
2019

IMC2019: Day 1, Problem 1

Problem 1. Evaluate the product

\(\displaystyle \prod_{n=3}^{\infty}\frac{(n^3+3n)^2}{n^6-64} .\)

Proposed by Orif Ibrogimov, ETH Zurich and National University of Uzbekistan and

Karen Keryan, Yerevan State University and American University of Armenia, Yerevan

Hint: Telescoping product.

  Solution