Determine all functions
from the set of positive integers to the set of positive integers such that, for all positive integers
and
, there exists a non-degenerate triangle with sides of lengths
(A triangle is non-degenerate if its vertices are not collinear.)
Proposed by Bruno Le Floch, France
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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
$$a, f(b) \text{ and } f(b + f(a) - 1).$$
(A triangle is non-degenerate if its vertices are not collinear.)
Proposed by Bruno Le Floch, France
Školjka