Let denote the set of all positive integers. Prove that there exists a unique function satisfying for all and in What is the value of
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Let $\mathbb{N}$ denote the set of all positive integers. Prove that there exists a unique function $f: \mathbb{N} \mapsto \mathbb{N}$ satisfying
$$f(m + f(n)) = n + f(m + 95)$$
for all $m$ and $n$ in $\mathbb{N}.$ What is the value of $\sum^{19}_{k = 1} f(k)?$
Izvor: Međunarodna matematička olimpijada, shortlist 1995
Školjka 
denote the set of all positive integers. Prove that there exists a unique function 
satisfying 
and 
in 
What is the value of 