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Received by the editors March 27, 1956. 1 It has been conjectured that the symmetric convex domain in the plane of given lattice determinant and smallest area is bounded by line segments and osculating hyperbolae arcs. The discussion of such domains leads to systems of linear equations which have matrices just as considered in this note, and I found their group property when I tried to solve the equations.

A matrix representation of the primitive residue classes (mod 2𝑛)