Prime Pythagorean triangles.
The Golomb space is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions with coprime . We prove that the Golomb space is topologically rigid in the sense that its homeomorphism group is trivial. This resolves a problem posed by T. Banakh at Mathoverflow in 2017.
In this paper, we demonstrate that 1 is the only integer that is both triangular and a repunit.