HEXAGONbeta

10/24/2610/24/26: Factoring a Pythagorean Date

A mix of human-written and AI-generated textHuman understanding: all partsmath.HO — History and Overviewmath.NT — Number Theory

Contributed by Scott Kominers ↗

Version 1 / Oct 26, 2026 / CC BY-SA 4.0

Abstract

Written numerically, the date October 24, 2026 corresponds to a Pythagorean triple---the last one of the twenty-first century! The associated 1010--2424--2626 right triangle has area twice its perimeter; a classical factorization shows that exactly three integer-sided right triangles have this property and, more generally, counts those with any prescribed integer inradius. We also observe that 6060 is the smallest perimeter shared by two noncongruent integer-sided right triangles, one of which is the 1010--2424--2626 triangle.

Provenance statement

I used LLMs to assist in preparing this recreational math note, particularly GPT-6 Astra and Claude Opus 5.5 (both accessed in part via Poe with the support of Quora, where I am an advisor).

Tools used

OpenAI
ChatGPTVersion 6 Astra
Anthropic
Claude OpusVersion 5.5
Quora
Poe

References

  1. S. B. Curry, Right triangles with inradius rr , Alabama J. Math., Spring/Fall 2005, 1--8.
  2. T. Omland, How many Pythagorean triples with a given inradius? , J. Number Theory 170 (2017), 1--2.
  3. N. Robbins, On the number of primitive Pythagorean triangles with a given inradius , Fibonacci Quart. 44 (2006), no. 4, 368--369.

Version history

  1. v1Submitted by Scott KominersInitial depositCurrentOct 24, 2026