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Diophantine - Infinitely many solutions

Source: Canadian Mathematical Olympiad - 1995 - Problem 4.

May 9, 2011
number theoryDiophantine equationnumber theory unsolved

Problem Statement

Let nn be a constant positive integer. Show that for only non-negative integers kk, the Diophantine equation ∑i=1nxi3=y3k+2\sum_{i=1 }^{n}{ x_i ^3}=y^{3k+2} has infinitely many solutions in the positive integers xi,yx_i, y.
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