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Infinite descent

Source: Korea National Olympiad 2009 Problem 3

September 9, 2012
number theoryDiophantine equationnumber theory proposed

Problem Statement

Let nn be a positive integer. Suppose that the diophantine equation zn=8x2009+23y2009z^n = 8 x^{2009} + 23 y^{2009} uniquely has an integer solution (x,y,z)=(0,0,0)(x,y,z)=(0,0,0). Find the possible minimum value of nn.
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