MathDB
Three numbers cannot be squares simultaneously

Source: APMO 2011

May 18, 2011
inequalitiesquadraticsnumber theory proposednumber theory

Problem Statement

Let a,b,ca,b,c be positive integers. Prove that it is impossible to have all of the three numbers a2+b+c,b2+c+a,c2+a+ba^2+b+c,b^2+c+a,c^2+a+b to be perfect squares.
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