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--- pow:problem5f24 [2024/11/03 21:34] – created mazur
+++ pow:problem5f24 [2024/11/19 07:43] (current) – mazur
@@ Line 1: / Line 1: @@
+<box 85% round orange|Problem 5 (due on Monday, November 4). >
+Let
+\[a_n=\sqrt[n^2]{\prod_{i=1}^n\prod_{j=1}^n \gcd(i,j)},\]
+where $\gcd(i,j)$ is the greatest common divisor of $i$ and $j$.
+Prove that the sequence $a_n$ converges.
+</box>
+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 {{:pow:2024fproblem5.pdf|Solution}}.