Ljunggren's trinomials and matrix equation $A^{x}+A^{y}=A^{z}$

Aleksander Grytczuk, Jaroslaw Grytczuk
2002 Tsukuba Journal of Mathematics  
We give some necessary and su‰cient conditions for solvability of the matrix equation (*) A x þ A y ¼ A z , with certain restrictions on integers x; y; z and a matrix A A M k ðZÞ, by applying Ljunggen's result on trinomials. Moreover, we obtain full solution of (*) for the case k ¼ 2 by another technique. 1999 Mathematics Subject Classification. Primary 11C20; Secondary 11D41.
doi:10.21099/tkbjm/1496164422 fatcat:eaxn3n2m5fcare3waev5vu7zkm