Three colours of Pythagorean triangles
Bulletin Polish Acad. Sci. Math.
MSC: Primary 05C15; Secondary 11D25
DOI: 10.4064/ba260209-28-8
Published online: 6 October 2026
Abstract
For any colouring of the set of all Pythagorean triangles with three colours there exist three Pythagorean triangles $\varDelta _1, \varDelta _2,\varDelta _3$ of the same colour satisfying $$ A(\varDelta _1) A(\varDelta _2) A(\varDelta _3)=t^2, $$ where $A(\varDelta )$ denotes the area of the triangle $\varDelta $ and $t\in \mathbb N$. This provides a counterpart to Fermat’s right triangle theorem.
