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Omni-MATH / Determine all functions f from the set of positive integers to the set of positive integers such that, for all positive integers a and b, there exists a non-degenerate triangle wit…

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problem

Determine all functions f f from the set of positive integers to the set of positive integers such that, for all positive integers a a and b b, there exists a non-degenerate triangle with sides of lengths \[ a, f(b) \text{ and } f(b \plus{} f(a) \minus{} 1).\] (A triangle is non-degenerate if its vertices are not collinear.) [i]
Plain-text mathematical notation (without MathML)
Determine all functions f from the set of positive integers to the set of positive integers such that, for all positive integers a and b, there exists a non-degenerate triangle with sides of lengths
\[ a, f(b) \text{ and } f(b \plus{} f(a) \minus{} 1).\]
(A triangle is non-degenerate if its vertices are not collinear.)

[i]
Original LaTeX notation
Determine all functions $ f$ from the set of positive integers to the set of positive integers such that, for all positive integers $ a$ and $ b$, there exists a non-degenerate triangle with sides of lengths
\[ a, f(b) \text{ and } f(b \plus{} f(a) \minus{} 1).\]
(A triangle is non-degenerate if its vertices are not collinear.)

[i]

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Source and history

task_id
ae723e11-1ecf-529b-8e6c-d0b66d4191dc
task_key
test--ae723e11-1ecf-529b-8e6c-d0b66d4191dc
task_revision_id
1
config / split
/ test

Official source

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