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2013 China Western Mathematical Olympiad ,Problem 1

Source: China Lanzhou 17 Aug 2013

August 17, 2013
modular arithmeticnumber theory proposednumber theory

Problem Statement

Does there exist any integer a,b,ca,b,c such that a2bc+2,ab2c+2,abc2+2a^2bc+2,ab^2c+2,abc^2+2 are perfect squares?
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