A Short Proof of Cauchy's Polygonal Number Theorem

DOI10.2307/2046263zbMath0611.10036OpenAlexW4250230226WikidataQ56442119 ScholiaQ56442119MaRDI QIDQ3751668

Melvyn B. Nathanson

Publication date: 1987

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2307/2046263

zbMATH Keywords

sums of squaresrepresentation of integerspolygonal numbersCauchy- Fermat theoremsum of polygonal numbers

Mathematics Subject Classification ID

Additive bases, including sumsets (11B13) Fibonacci and Lucas numbers and polynomials and generalizations (11B39) Additive number theory; partitions (11P99)

Related Items (8)

A New Polygonal Number Theorem ⋮ Numerical semigroups generated by quadratic sequences ⋮ Weighted sums of generalized polygonal numbers with coefficients $1$ or $2$ ⋮ On universal sums of polygonal numbers ⋮ The pentagonal theorem of sixty-three and generalizations of Cauchy's lemma ⋮ Representing \(n\) as \(n=x+y+z\) with \(x^2+y^2+z^2\) a square ⋮ On sums of four pentagonal numbers with coefficients ⋮ The triangular theorem of eight and representation by quadratic polynomials

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