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]. geometryperimeterfloor functioncombinatorics unsolvedcombinatorics