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Problem 5 (due on Monday, November 4).
Let an=n2√n∏i=1n∏j=1gcd(i,j), where gcd(i,j) is the greatest common divisor of i and j. Prove that the sequence an converges.
The problem was solved by Prof. Vladislav Kargin and Dr. Mathew Wolak (who submitted two solutions). The submitted solutions are similar to our two in-house solutions. For details see the following link Solution.