MathDB

Number of distinct, incongruent, integer-sided triangles

Source: IMO Longlist 1989, Problem 49

September 18, 2008

geometryperimeterfloor functioncombinatorics unsolvedcombinatorics

Problem Statement

Let

t(n)

for n \equal{} 3, 4, 5, \ldots, represent the number of distinct, incongruent, integer-sided triangles whose perimeter is

n;

e.g., t(3) \equal{} 1. Prove that t(2n\minus{}1) \minus{} t(2n) \equal{} \left[ \frac{6}{n} \right] \text{ or } \left[ \frac{6}{n} \plus{} 1 \right].