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- Feb 14, 2012

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For any natural number $n$, ($n\ge 3$), 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. $f(2000)=f(1997)$.

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