Abstract
Let d(n) denote the corank of I + A over the field with two elements, where A is the adjacency matrix of the discrete torus Cn × Cn , and I is the identity matrix. We shall prove that d(2n) = 2d(n) and d(2 r + 1) = d(2 r − 1) + 4. For the proof of the latter result, we use an elliptic curve. Our motivation for this study is the “lights out” puzzle.
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