  An open conjecture of Erdos and Moser is that the only solution of the
Diophantine equation in the title is the trivial solution 1+2=3. Reducing the
equation modulo k and k^2, we give necessary and sufficient conditions on
solutions to the resulting congruence and supercongruence. A corollary is a new
proof of Moser's result that the conjecture is true for odd exponents n. We
also connect solutions k of the congruence to primary pseudoperfect numbers and
to a result of Zagier. The proofs use divisibility properties of power sums as
well as Lerch's relation between Fermat and Wilson quotients.
