Abstract
We give some necessary and sufficient conditions for solvability of the matrix equation (*) $A^x + A^{y}=A^{z}$, with certain restrictions on integers $x, y, z$ and a matrix $A \in M_{k}(\bm{Z})$, by applying Ljunggen's result on trinomials. Moreover, we obtain full solution of (*) for the case $k=2$ by another technique.
Citation
Aleksander Grytczuk. Jaroslaw Grytczuk. "Ljunggren's trinomials and matrix equation $A^{x}+A^{y}=A^{z}$." Tsukuba J. Math. 26 (2) 229 - 235, December 2002. https://doi.org/10.21099/tkbjm/1496164422
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