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Omni-MATH / Find all integers n≥3 such that the following property holds: if we list the divisors of n! in increasing order as 1=d₁<d₂<⋯<d_(k)=n! , then we have d₂−d₁≤d₃−d₂≤⋯≤d_(k)−d_(k−1). Co…

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problem

Find all integers n≥3n \geq 3 such that the following property holds: if we list the divisors of n!n ! in increasing order as 1=d1<d2<⋯<dk=n!1=d_1<d_2<\cdots<d_k=n! , then we have d2−d1≤d3−d2≤⋯≤dk−dk−1.d_2-d_1 \leq d_3-d_2 \leq \cdots \leq d_k-d_{k-1} . Contents 1 Solution (Explanation of Video) 2 Solution 2 3 Video Solution 4 See Also
Plain-text mathematical notation (without MathML)
Find all integers n≥3 such that the following property holds: if we list the divisors of n! in increasing order as 1=d₁<d₂<⋯<d_(k)=n! , then we have d₂−d₁≤d₃−d₂≤⋯≤d_(k)−d_(k−1). 
Contents   1  Solution (Explanation of Video)  2  Solution 2  3  Video Solution  4  See Also
Original LaTeX notation
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 \[d_2-d_1 \leq d_3-d_2 \leq \cdots \leq d_k-d_{k-1} .\] 
Contents   1  Solution (Explanation of Video)  2  Solution 2  3  Video Solution  4  See Also

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Source and history

task_id
4cda72f7-4ddf-522f-ada6-05c883b187dc
task_key
test--4cda72f7-4ddf-522f-ada6-05c883b187dc
task_revision_id
1
config / split
/ test

Official source

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