## Tsukuba Journal of Mathematics

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

#### 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.

#### Article information

Source
Tsukuba J. Math., Volume 26, Number 2 (2002), 229-235.

Dates
First available in Project Euclid: 30 May 2017

https://projecteuclid.org/euclid.tkbjm/1496164422

Digital Object Identifier
doi:10.21099/tkbjm/1496164422

Mathematical Reviews number (MathSciNet)
MR1940392

Zentralblatt MATH identifier
1020.11019

#### Citation

Grytczuk, Aleksander; Grytczuk, Jaroslaw. Ljunggren's trinomials and matrix equation $A^{x}+A^{y}=A^{z}$. Tsukuba J. Math. 26 (2002), no. 2, 229--235. doi:10.21099/tkbjm/1496164422. https://projecteuclid.org/euclid.tkbjm/1496164422