Centered polygonal number theorem

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Last edited by Qwerfjkl (bot) (talk | contribs) 9 days ago. (Update)

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In additive number theory, the centered polygonal number theorem states that every positive integer is a sum of at most $n+2$ $n$ -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]

Cite error: A <ref> tag is missing the closing </ref> (see the help page).

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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[1] 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.

[2] 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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