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Standard morphisms and Pythagorean triples — arXiv:2608.11975

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.11975
License (as archived): CC0-1.0
Archived: 2026-10-19T05:47:45.904Z
SHA-256 of the archived text: 8241e5786f721b2cbf1b588e0a2ba8473a10d545374fb1a406f385f68248bf68
Stable URL of this page: https://metraipolis.com/documento/dc_de751eef6960

How to cite

Standard morphisms and Pythagorean triples — arXiv:2608.11975 — arXiv (en), https://arxiv.org/abs/2608.11975 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_de751eef6960 (Metraipolis archive dc_de751eef6960, sha256 8241e5786f721b2cbf1b588e0a2ba8473a10d545374fb1a406f385f68248bf68)

BibTeX

@misc{dcde751eef6960,
  title = {Standard morphisms and Pythagorean triples — arXiv:2608.11975},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.11975},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_de751eef6960; sha256 8241e5786f721b2cbf1b588e0a2ba8473a10d545374fb1a406f385f68248bf68},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.11975. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Let $m\geq 1$, let $f:\mathbb N\to\mathbb Z/m\mathbb Z$ be a standard morphism and let $T(m)$ be the least integer $N$ such that every such $f$ admits a primitive monochromatic Pythagorean triple with hypotenuse at most $N$. The aim of this note is to prove that every standard morphism has infinitely many identity-valued Pythagorean triples and infinitely many primitive monochromatic Pythagorean triples. Thus the qualitative part of Problem~4.3 of Eliahou, Fromentin, Marion-Poty and Robilliard is solved for every $m$. Moreover, $T(m)$ is finite, the morphism $n\mapsto v_3(n)\pmod m$ has least possible hypotenuse $(9^m+1)/2$ and $T(d)\leq T(m)$ when $d\mid m$.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-08-13 in math.CO).
Categorie arXiv: Combinatorics (math.CO).
Pagina del lavoro: https://arxiv.org/abs/2608.11975 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:40:33.656Z dalla pagina https://arxiv.org/catchup/math.CO/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).