  We prove that the signature of an even, symmetric form on a finite rank
integral lattice, has signature divisible by 8, provided its associated linking
form vanishes in the Witt group of linking forms. Our result generalizes the
well know fact that an even, unimodular form has signature divisible by 8.
  We give applications to signatures of 4n-dimensional manifolds, signatures of
classical knots, and provide new restrictions to solutions of certain
Diophantine equations.
