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Omni-MATH / Let n≥1 be an odd integer. Determine all functions f from the set of integers to itself, such that for all integers x and y the difference f(x)−f(y) divides x^(n)−y^(n). [i]

Problem

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problem

Let n≥1n \geq 1 be an odd integer. Determine all functions ff from the set of integers to itself, such that for all integers xx and yy the difference f(x)−f(y)f(x)-f(y) divides xn−yn.x^n-y^n. [i]
Plain-text mathematical notation (without MathML)
Let n≥1 be an odd integer. Determine all functions f from the set of integers to itself, such that for all integers x and y the difference f(x)−f(y) divides x^(n)−y^(n).

[i]
Original LaTeX notation
Let $n \geq 1$ be an odd integer. Determine all functions $f$ from the set of integers to itself, such that for all integers $x$ and $y$ the difference $f(x)-f(y)$ divides $x^n-y^n.$

[i]

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Source and history

task_id
eba4fd3e-0239-59eb-a641-2ce2cab8ee4a
task_key
test--eba4fd3e-0239-59eb-a641-2ce2cab8ee4a
task_revision_id
1
config / split
/ test

Official source

initial import