An algebra problem by Shubham Haldēr

Algebra Level 4

Suppose that \(a, b\) and \(c\) are non-zero numbers that satisfy

\[ \dfrac1a + \dfrac1b + \dfrac1c = \dfrac1{a+b+c}. \]

If \(n\) is an integer such that

\[ \dfrac1{a^n} + \dfrac1{b^n} + \dfrac1{c^n} = \dfrac1{a^n+b^n+c^n}, \]

then what is the best classification of \(n\)?

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