# 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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