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IMC 2018 P3

Source: IMC 2018 P3

July 24, 2018
linear algebraimc2018

Problem Statement

Determine all rational numbers aa for which the matrix (a−a−10a−a0−110a−a01a−a)\begin{pmatrix} a & -a & -1 & 0 \\ a & -a & 0 & -1 \\ 1 & 0 & a & -a\\ 0 & 1 & a & -a \end{pmatrix} is the square of a matrix with all rational entries.
Proposed by Daniël Kroes, University of California, San Diego
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