Molnar originally posed the following problem to construct two k x
k matrices such that:
/a_11 ... a_1k\ /(a_11)^2 ... (a_1k)^2\
det ( ... ... ... ) = 1, det ( ... ... ... ) = +/- 1
\a_k1 ... a_kk/ \(a_k1)^2 ... (a_kk)^2/
where the a_ii are integers not equal to plus or minus 1, and `det'
denotes the
determinant
of a matrix. The solutions to this problem are significant in classifying certain types
of topological spaces. Guy discusses a variant where 0 entries are also
disallowed and the sign of both determinants must be positive.