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Omni-MATH / Let f(x)=x²+x+1. Determine, with proof, all positive integers n such that f(k) divides f(n) whenever k is a positive divisor of n.

Problem

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problem

Let f(x)=x2+x+1f(x)=x^{2}+x+1. Determine, with proof, all positive integers nn such that f(k)f(k) divides f(n)f(n) whenever kk is a positive divisor of nn.
Plain-text mathematical notation (without MathML)
Let f(x)=x²+x+1. Determine, with proof, all positive integers n such that f(k) divides f(n) whenever k is a positive divisor of n.
Original LaTeX notation
Let $f(x)=x^{2}+x+1$. Determine, with proof, all positive integers $n$ such that $f(k)$ divides $f(n)$ whenever $k$ is a positive divisor of $n$.

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Source and history

task_id
0aa35000-2fab-5ce9-9f29-adeee27cb3c2
task_key
test--0aa35000-2fab-5ce9-9f29-adeee27cb3c2
task_revision_id
1
config / split
/ test

Official source

initial import