A Formula For All K-Gonal Numbers that Are Centered
Jawad Sadek, Russell Euler
TL;DR
This paper derives a closed-form formula for all k-gonal numbers that are also centered k-gonal, unifying two classes of polygonal numbers through a mathematical expression.
Contribution
It provides the first explicit formula linking k-gonal and centered k-gonal numbers for any positive integer k.
Findings
Derived a closed-form formula for centered k-gonal numbers
Unified the understanding of k-gonal and centered k-gonal numbers
Applicable to all positive integers k
Abstract
Fix a positive integer k. In this paper, we give a formula in closed form for all k-polygonal numbers that are also centered k-polygonal.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematics and Applications · Analytic Number Theory Research