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INTEGER POLYGONS OF GIVEN PERIMETER
- Part of
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- Journal:
- Bulletin of the Australian Mathematical Society / Volume 100 / Issue 1 / August 2019
- Published online by Cambridge University Press:
- 30 January 2019, pp. 131-147
- Print publication:
- August 2019
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- Article
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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).
