# Solution: 2022-23 The number of eigenvalues of 8 by 8 matrices

Let $$A$$ be an 8 by 8 integral unimodular matrix. Moreover, assume that for each $$x \in \mathbb{Z}^8$$, we have $$x^{\top} A x$$ is even. What is the possible number of positive eigenvalues for $$A$$?

The best solution was submitted by Noitnetta Yobepyh (Snaejwen High School, +4). Congratulations!

Other solutions were submitted by 김기수 (KAIST 수리과학과 18학번, +3), 여인영 (KAIST 물리학과 20학번, +3).

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