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Omni-MATH / Denote by N the set of all positive integers. Find all functions f:N→N such that for all positive integers m and n, the integer f(m)+f(n)−mn is nonzero and divides mf(m)+nf(n). [i]

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problem

Denote by N\mathbb{N} the set of all positive integers. Find all functions f:N→Nf:\mathbb{N}\rightarrow \mathbb{N} such that for all positive integers mm and nn, the integer f(m)+f(n)−mnf(m)+f(n)-mn is nonzero and divides mf(m)+nf(n)mf(m)+nf(n). [i]
Plain-text mathematical notation (without MathML)
Denote by N the set of all positive integers. Find all functions f:N→N such that for all positive integers m and n, the integer f(m)+f(n)−mn is nonzero and divides mf(m)+nf(n).

[i]
Original LaTeX notation
Denote by $\mathbb{N}$ the set of all positive integers. Find all functions $f:\mathbb{N}\rightarrow \mathbb{N}$ such that for all positive integers $m$ and $n$, the integer $f(m)+f(n)-mn$ is nonzero and divides $mf(m)+nf(n)$.

[i]

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Source and history

task_id
ec0738cf-cdfb-5f11-b227-ad1d5f7ed7eb
task_key
test--ec0738cf-cdfb-5f11-b227-ad1d5f7ed7eb
task_revision_id
1
config / split
/ test

Official source

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