Centered polygonal number theorem
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In additive number theory, the centered polygonal number theorem states that every positive integer is a sum of at most n+2 centered n-gonal numbers.
History
In 1850, Sir Frederick Pollock conjectured that every positive integer is the sum of at most 11 centered nonagonal numbers. This conjecture was confirmed as true by Miroslav Kureš in 2023. [1]
The result was generalized to the above theorem by Benjamin Lee Warren and Miroslav Kureš in 2025. [2]
References
- ^ Kureš, Miroslav (2023-10-27). "A Proof of Pollock's Conjecture on Centered Nonagonal Numbers". The Mathematical Intelligencer. 46 (3): 234–235. doi:10.1007/s00283-023-10307-0. ISSN 0343-6993.
- ^ Warren, Benjamin Lee; Kureš, Miroslav (2025-06-09). "Every Positive Integer Is a Sum of at most n+2 Centered n-gonal Numbers". Mathematica Slovaca. 75 (3): 515–524. doi:10.1515/ms-2025-0037. ISSN 0139-9918.