Symmetric Pythagorean triple preserving matrices.(English)Zbl 1031.11013

Authors’ abstract: A Pythagorean Triple Preserving Matrix (PTPM) is a $$3\times 3$$ matrix with integer entries such that if it is multiplied by a Pythagorean triple, the result is also a Pythagorean triple. Necessary and sufficient conditions for a PTPM to be symmetric are given. Monoids of Symmetric PTPMs (SPTPM) with positive integer entries are developed, and to ensure that the set is closed under matrix multiplication, the focus is in finding commutative SPTPMs.

MSC:

 11C20 Matrices, determinants in number theory 15B36 Matrices of integers 11D09 Quadratic and bilinear Diophantine equations