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 λ2, 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: λ1= 2λ2 mod 24.
Dedicated to Rob Kirby on the occasion
of his 60th birthday.