Unstable homotopy theory 2 — Determine the v_1 -exponents for the spheres.

Determine the v_1 -exponents for the spheres. Recall that Cohen, Moore, and Neisendorfer showed that the p-torsion in the homotopy of S^2n+1 is all killed by p^n, but not p^n-1, for odd p. Determine the analogous v_1-exponent. I am not quite clear on the statement of this problem; I think we want to look at maps from the Moore space into X, so that the Adams map actually acts. There is probably a conjecture out there about what the exponent should be, but again I do not know it. Hopefully somebody will let me know and I can clean up this problem.