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OlympiadBench / 1800 / Find all positive integers n with the following property: the k positive…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

Find all positive integers

n

with the following property: the

k

positive divisors of

n

have a permutation

\left(d_{1}, d_{2}, \ldots, d_{k}\right)

such that for every

i=1,2, \ldots, k

, the number

d_{1}+\cdots+d_{i}

is a perfect square.

Plain-text mathematical notation (without MathML)

Find all positive integers n with the following property: the k positive divisors of n have a permutation (d₁,d₂,…,d_(k)) such that for every i=1,2,…,k, the number d₁+⋯+d_(i) is a perfect square.

Original LaTeX notation

Find all positive integers $n$ with the following property: the $k$ positive divisors of $n$ have a permutation $\left(d_{1}, d_{2}, \ldots, d_{k}\right)$ such that for every $i=1,2, \ldots, k$, the number $d_{1}+\cdots+d_{i}$ is a perfect square.

answer type

Numerical

is multiple answer

true

language

English

question type

Open-ended

subject

Math

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Source and history

upstream_id / Original problem ID: 1800
task_id: e91d833f-6202-5a82-9621-d1c6f5109a1b
task_key: OE~5fTO~5fmaths~5fen~5fCOMP--train--1800
task_revision_id: 3
config / split: OE_TO_maths_en_COMP / train

Official source

initial import