INMO 2000 Problem 6

For any natural number $n,(n \geq 3)$, let $f(n)$ denote the number of non-congruent integer-sided triangles with perimeter $n$ (e.g., $f(3)=1, f(4)=0, f(7)=2$ ). Show that

(a) $f(1999)>f(1996)$

(b) $f(2000)=f(1997)$.