Published online by Cambridge University Press: 30 January 2019
A classical result of Honsberger states that the number of incongruent triangles with integer sides and perimeter $n$ is the nearest integer to
$n^{2}/48$ (
$n$ even) or
$(n+3)^{2}/48$ (
$n$ odd). We solve the analogous problem for
$m$-gons (for arbitrary but fixed
$m\geq 3$) and for polygons (with arbitrary number of sides).