Centered polygonal number theorem
In additive number theory, the centered polygonal number theorem states that every positive integer is a sum of at most n+2 n-gonal numbers.
History
In 1850, Sir_Frederick_Pollock,_1st_Baronet 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]
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The result was generalized 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. 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. doi:10.1515/ms-2025-0037. ISSN 0139-9918.
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