# Averaging Sums of Powers of Integers

by Thomas J. Pfaff

College Mathematics Journal
November, 2011

Subject classification(s): Algebra and Number Theory | Number Theory | Diophantine Equations
Applicable Course(s): 4.3 Number Theory

When is the average of sums of powers of integers itself a sum of the ﬁrst $n$ integers raised to a power? We provide all solutions when averaging two sums, and provide some conditions regarding when larger averages may have solutions.

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