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arXiv · 2607.03618

A Combinatorial Proof for Partitions of Pythagorean Triples Into Three Parts

Ivan V. Morozov
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Abstract

Any Pythagorean triple $\{a,b,c\}$ such that $a^{2}+b^{2}=c^{2}$ satisfies an elegant relation between its partitions into three parts, namely $p(a,3)+p(b,3)=p(c,3)$. While this property follows from elementary analytic methods, we give the first combinatorial proof of this relation.

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Ivan V. Morozov. 2026-07-03. A Combinatorial Proof for Partitions of Pythagorean Triples Into Three Parts. https://arxiv.org/abs/2607.03618

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