A Top Hat for Moser's Four Mathemagical Rabbits
A Top Hat for Moser's Four Mathemagical Rabbits
P. Moree
TLDR
It is shown here that Moser's result can be derived from a von Staudt-Clausen type theorem and the mathematical arguments used in the proofs were already available during the lifetime of Lagrange.
Abstract
Abstract If the equation 1k +2k + … + (m - 2) k + (m - 1) k = mk has a solution with k ≥ 2, then m > 10106. 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).