MathDB

15

Part of 1984 IMO Longlists

Problems(1)

Minimum of sum or difference of fifth powers

Source:

10/9/2010
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?
number theory unsolvednumber theory