Question 5
Find all functions $f \colon \mathbb{Z}_{\gt 0} \to \mathbb{Z}_{\gt 0}$ such that for positive integers $a$ and $b$, the numbers $$
a, \qquad f(b), \qquad f(b+f(a)-1)
$$ are the sides of a non-degenerate triangle. A triangle is non-degenerate if its vertices are not collinear.
a, \qquad f(b), \qquad f(b+f(a)-1)
$$ are the sides of a non-degenerate triangle. A triangle is non-degenerate if its vertices are not collinear.