MathLabs

Problem 1

Let a,b,ca,b,c be positive integers. Prove that it is impossible for all three numbers a2+b+ca^2+b+c, b2+c+ab^2+c+a, and c2+a+bc^2+a+b to be perfect squares.
Step 5 of 5: Conclusion
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impossible\boxed{\text{impossible}}
Detailed analysis

Thus the three displayed numbers cannot all be perfect squares.