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MathNet 2020 — Math Olympiad Vault — Part 03 Question 8

Math Olympiad Vault · MathNet 2020 — Math Olympiad Vault — Part 03

Question 8

Find the sum of all positive integers $n$ for which
$$
\frac{15 \cdot n!^{2}+1}{2 n-3}
$$
is an integer.