Cannonball Polygons with Multiplicities
Abstract
We generalize the Cannonball Problem by introducing integer-valued and non-increasing arithmetic functions w. We associate these functions w with certain polygons, which we call cannonball polygons. Through this correspondence, we show that for any Z∈N, there exists a cannonball polygon with multiplicity 8 and largest side of length Z. Moreover, for any multiplicity s greater than 8, we provide an asymptotic formula for the number of distinct classes of cannonball polygons with multiplicity s.
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