035: Molnar's Problem

Proposed by Alan Frisch, Chris Jefferson, Ian Miguel

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.