A partial solution was also received from Dayo Dada. Correct solutions were also received from Tim Kelly, Al Zimmermann, Robert T. McQuaid, Burkart Venzke, William Webb, Thomas Teo, CWLDOC, Tye Rattenbury, Jeff Duggins, Steven Young, Daniel Statman, Aaron Kahn.

Most solvers noted that the result is not true if a = 1 and N is even, but is otherwise correct.

Since N^a is the sum of N times the integer N^a-1 it is also the sum of N integers whose average is N^a-1. Take these integers to be the N odd integers centered at the odd integer N^a-1 - N + 1.

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Page last updated 27 February 1999.