  We consider the Cooper-problem on a two-dimensional, square lattice with a
uniform, perpendicular magnetic field. Only rational flux fractions are
considered. An extended (real-space) Hubbard model including nearest and next
nearest neighbor interactions is transformed to "k-space", or more precisely,
to the space of eigenfunctions of Harper's equation, which constitute basis
functions of the magnetic translation group for the lattice. A BCS-like
truncation of the interaction term is performed. Expanding the interactions in
the basis functions of the irreducible representations of the point group
$C_{4\nu}$ of the square lattice simplify calculations. The numerical results
indicate enhanced binding compared to zero magnetic field, and thus re-entrant
superconducting pairing at extreme magnetic fields, well beyond the point where
the usual semi-classical treatment of the magnetic field breaks down.
