Draft:Bpow55

Take any two positive integers <m>N</m> and <m>a</m>. Show that <m>N^a</m> is the sum of <m>N</m> consecutive odd integers.

As an easy example, note that

<m>7^{13} = 96889010407 = 13841287195 + 13841287197 + 13841287199 + 13841287201 + 13841287203 + 13841287205 + 13841287207</m>

Problem by Alberto L Delgado, from the now extinct Bradley Problem of the Week.