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Sum of 2014-th powers of 2015 integers

Source: Itamo 2014 - p5

December 1, 2014

algebra proposedalgebra

Problem Statement

Prove that there exists a positive integer that can be written, in at least two ways, as a sum of

2014

-th powers of

2015

distinct positive integers

x_1 <x_2 <\cdots <x_{2015}