  We show that if we suppose n>3 and the (2n-1)-stem in the stable homotopy
groups of spheres has no 2-torsion, then the Whitehead squares of the identity
maps of (2n+1) and (4n+3)-spheres are divisible by 2. Applying the result of G.
Wang and Z. Xu on the 61-stem in the stable homotopy groups of spheres, we find
that the Kervaire invariant one elements in dimensions 62 and 126 exist.
