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Omni-MATH / Given an integer k≥2, determine all functions f from the positive integers into themselves such that f(x₁)!+f(x₂)!+⋯f(x_(k))! is divisibe by x₁!+x₂!+⋯x_(k)! for all positive intege…

Problem

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problem

Given an integer k≥2k\geq 2, determine all functions ff from the positive integers into themselves such that f(x1)!+f(x2)!+⋯f(xk)!f(x_1)!+f(x_2)!+\cdots f(x_k)! is divisibe by x1!+x2!+⋯xk!x_1!+x_2!+\cdots x_k! for all positive integers x1,x2,⋯xkx_1,x_2,\cdots x_k. AlbaniaAlbania
Plain-text mathematical notation (without MathML)
Given an integer k≥2, determine all functions f from the positive integers into themselves such that f(x₁)!+f(x₂)!+⋯f(x_(k))! is divisibe by x₁!+x₂!+⋯x_(k)! for all positive integers x₁,x₂,⋯x_(k).

Albania
Original LaTeX notation
Given an integer $k\geq 2$, determine all functions $f$ from the positive integers into themselves such that $f(x_1)!+f(x_2)!+\cdots f(x_k)!$ is divisibe by $x_1!+x_2!+\cdots x_k!$ for all positive integers $x_1,x_2,\cdots x_k$.

$Albania$

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Source and history

task_id
47ee120d-2e68-5372-bd07-45d07a8cbc43
task_key
test--47ee120d-2e68-5372-bd07-45d07a8cbc43
task_revision_id
1
config / split
/ test

Official source

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