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How to explain the patterns in the matrix defined in François Brunault's answer to the question Freeness of a Z[x] module depicted below? -- Choosing colors according to the highest power of 2 which ...

Suppose $X$ and $Y$ are two $n$-circulants (Cayley graphs for $\mathbb{Z}_n$) with adjacency matrices $A_X$ and $A_Y$. Since they are circulants, both $X$ and $Y$ lie in some symmetric association ...

There are already detailed results on the solutions of linear equations over fields, but I'd like to inquire about any good conclusions regarding the solutions of linear equations over the integer ...