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Using elementary methods, we determine the highest power of 2 dividing apower sum 1^n + 2^n + . . . + m^n, generalizing Lengyel's formula for the casewhere m is itself a power of 2. An application is a simple proof of Moree'sresult that, if (a,m,n) is any solution of the generalized Erdos-MoserDiophantine equation 1^n + 2^n + . . . + (m-1)^n = am^n, then m is odd.

Divisibility of Power Sums and the Generalized Erdos-Moser Equation