Divizibilitate si ecuatie functionala
Posted: Sun Jul 13, 2008 8:41 pm
Gasiti functiile surjective \( f : \mathbb{N}^{\ast} \rightarrow \mathbb{N}^{\ast} \) astfel incat \( \forall m, n \in \mathbb{N}^{\ast} \) si \( p \) prim, \( p | f(m + n) \Leftrightarrow p | f(m) + f(n) \).
[ IMO Shortlist 2007, N5 ]
[ IMO Shortlist 2007, N5 ]