Ljunggren's trinomials and matrix equation \(A^x+A^y=A^z\) (Q1861070)
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scientific article; zbMATH DE number 1880961
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Ljunggren's trinomials and matrix equation \(A^x+A^y=A^z\) |
scientific article; zbMATH DE number 1880961 |
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Ljunggren's trinomials and matrix equation \(A^x+A^y=A^z\) (English)
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1 October 2003
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Some necessary and sufficient conditions for solvability of the matrix equation \(A^x + A^y = A^z\) are presented with certain restrictions on integers \(x, y, z\) and a matrix \(A \in M_k(\mathbb Z)\) by applying \textit{W. Ljunggren}'s [Math. Scand. 8, 65--70 (1960; Zbl 0095.01305)] result on trinomials. Moreover, a full solution of this equation is obtained for the case \(k = 2\) by another technique.
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matrix equation
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Ljunggren trinomials
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