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Perfect Square

Source: 2017 Greece National Olympiad Problem 3

May 2, 2017
algebranumber theory

Problem Statement

Find all integer triples (a,b,c)(a,b,c) with a>0>b>ca>0>b>c whose sum equal 00 such that the number N=2017−a3b−b3c−c3aN=2017-a^3b-b^3c-c^3a is a perfect square of an integer.
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