# Solution: 2022-20 4 by 4 symmetric integral matrices

Let $$S$$ be the set of all 4 by 4 integral positive-definite symmetric unimodular matrices. Define an equivalence relation $$\sim$$ on $$S$$ such that for any $$A,B \in S$$, we have $$A \sim B$$ if and only if $$PAP^\top = B$$ for some integral unimodular matrix $$P$$. Determine $$S ~/\sim$$.

The best solution was submitted by 김기수 (KAIST 수리과학과 18학번, +4). Congratulations!

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