  If the equation of the title has an integer solution with k>=2, then
m>10^{10^6}. Leo Moser showed this in 1953 by amazingly elementary methods.
With the hindsight of more than 50 years his proof can be somewhat simplified.
We give a further proof showing that Moser's result can be derived from a von
Staudt-Clausen type theorem. Based on more recent developments concerning this
equation, we derive a new result using the divisibility properties of numbers
in the sequence 2^{2e+1}+1, e=0,1,2,..... In the final section we show that
certain Erdos-Moser type equations arising in a recent paper of Kellner can be
solved completely.
