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Algebra Level pending

Let \(a,b,c\) three distinct nonzero real numbers such that

\[a+\frac { 1 }{ b } =b+\frac { 1 }{ c } =c+\frac { 1 }{ a } \]

find \(\left| abc \right| \)


This question is flagged because such a scenario cannot occur, which makes the question pointless.

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