  We show that there exist infinitely many pairs of distinct knots in the
3-sphere such that each pair can yield homeomorphic lens spaces by the same
Dehn surgery. Moreover, each knot of the pair can be chosen to be a torus knot,
a satellite knot or a hyperbolic knot, except that both cannot be satellite
knots simultaneously. This exception is shown to be unavoidable by the
classical theory of binary quadratic forms.
