pow:problem5f24
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| pow:problem5f24 [2024/11/19 04:17] – mazur | pow:problem5f24 [2024/11/19 07:43] (current) – mazur | ||
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| + | <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, | ||
| + | where $\gcd(i,j)$ is the greatest common divisor of $i$ and $j$. | ||
| + | Prove that the sequence $a_n$ converges. | ||
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| + | </ | ||
| + | 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 {{: | ||
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