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Minimum of sum or difference of fifth powers

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October 9, 2010
number theory unsolvednumber theory

Problem Statement

Consider all the sums of the form ∑k=11985ekk5=±15±25±⋯±19855\displaystyle\sum_{k=1}^{1985} e_kk^5=\pm 1^5\pm 2^5\pm\cdots\pm1985^5 where ek=±1e_k=\pm 1. What is the smallest nonnegative value attained by a sum of this type?
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