Fermat limit and congruence of Ohtsuki invariants

By calculating the Fermat limit of certain q-Fermat functions, we get explicit surgery formulae for the second and third Ohtsuki invariants for homology 3-spheres. The surgery formula of the second Ohtsuki invariant \lambda _2, combined with an argument using the general theory of finite type invariants of homology 3-spheres, leads to a congruence relation between the first and second Ohtsuki invariants: \lambda _1=2\lambda _2 mod 24.