A top hat for Moser's four mathemagical rabbits

Abstract

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).

7 pages. Meanwhile MacMillan and Sondow showed that Lagrange (1736-1813). can be replaced by Pascal (1623-1662)

Cited by in corpus (1)

• Moser's mathemagical work on the equation 1^k+2^k+...+(m-1)^k=m^k