  If the equation 1^k+2^k+...+(m-2)^k+(m-1)^k=m^k has an integer solution with
k>1, then m>10^{10^6}. Leo Moser showed this in 1953 by remarkably elementary
methods. His proof rests on four identities he derives separately. It is shown
here that Moser's result can be derived from a von Staudt-Clausen type theorem
(an easy proof of which is also presented here). In this approach the four
identities can be derived uniformly. The mathematical arguments used in the
proofs were already available during the lifetime of Lagrange (1736-1813).
