[dektep]

1. Find all functions $f:\mathbb{R}\to\mathbb{R}$ satisfying $f(x+f(y))=x+f(f(y))$
for all real numbers $x$ and $y$, with the additional constraint f(2004)=2005.

2. Let $\mathbb{N}$ denote the set of positive integers.Find all functions $f:\mathbb{N}\to\mathbb{N}$
such that $f(m+n)f(m-n)=f(m^2)$.

3. Find all functions $f:\mathbb{R}\to\mathbb{R}$ such that $f(x)f(yf(x)-1)=x^2f(y)-f(x)$
for all real numbers $x$ and $y$.