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2024 USAMO Problems/Problem 1

Find all integers $n \geq 3$ such that the following property holds: if we list the divisors of $n !$ in increasing order as $1=d_1<d_2<\cdots<d_k=n!$, then we have \[d_2-d_1 \leq d_3-d_2 \leq \cdots \leq d_k-d_{k-1} .\]

Video Solution

https://youtu.be/ZcdBpaLC5p0 [video contains problem 1 and problem 4]

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