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Omni-MATH / Determine all composite integers n>1 that satisfy the following property: if d₁, d₂, …, d_(k) are all the positive divisors of n with 1=d₁<d₂<⋯<d_(k)=n, then d_(i) divides …

Problem

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problem

Determine all composite integers n>1n>1 that satisfy the following property: if d1d_1, d2d_2, …\ldots, dkd_k are all the positive divisors of nn with 1=d1<d2<⋯<dk=n1 = d_1 < d_2 < \cdots < d_k = n, then did_i divides di+1+di+2d_{i+1} + d_{i+2} for every 1≤i≤k−21 \leq i \leq k - 2.
Plain-text mathematical notation (without MathML)
Determine all composite integers n>1 that satisfy the following property: if d₁, d₂, …, d_(k) are all the positive divisors of n with 1=d₁<d₂<⋯<d_(k)=n, then d_(i) divides d_(i+1)+d_(i+2) for every 1≤i≤k−2.
Original LaTeX notation
Determine all composite integers $n>1$ that satisfy the following property: if $d_1$, $d_2$, $\ldots$, $d_k$ are all the positive divisors of $n$ with $1 = d_1 < d_2 < \cdots < d_k = n$, then $d_i$ divides $d_{i+1} + d_{i+2}$ for every $1 \leq i \leq k - 2$.

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Source and history

task_id
a82e8299-5043-54b0-b1bf-b62f254d85f5
task_key
test--a82e8299-5043-54b0-b1bf-b62f254d85f5
task_revision_id
1
config / split
/ test

Official source

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