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Find no of triangles

Source: INMO 2000 Problem 6

October 10, 2005
geometryperimeterinequalitiestriangle inequalitycombinatorics unsolvedcombinatorics

Problem Statement

For any natural numbers nn, ( n≥3n \geq 3), let f(n)f(n) denote the number of congruent integer-sided triangles with perimeter nn. Show that (i) f(1999)>f(1996)f(1999) > f (1996); (ii) f(2000)=f(1997)f(2000) = f(1997).
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