MathNet 2000 — Math Olympiad Vault Question 101

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. $f(1999) \gt f(1996)$

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