# Variation on Fermat's Last Theorem

I've already heard about how Fermat stated that no three positive integers $$a$$, $$b$$ and $$c$$ can satisfy the equation $$a^n + b^n = c^n$$ for any value of $$n>2$$. I think Andrew Wiles proved that this conjecture was true.

Now, I'm wondering whether any three positive integers $$a$$, $$b$$ and $$c$$ can satisfy the equation $$\frac {1}{a^n}$$ + $$\frac {1}{b^n}$$ = $$\frac {1}{c^n}$$ for any value of $$n>2$$.

If this is possible tell me why it is possible.

If this is impossible tell me why it is impossible.

2 years, 5 months ago

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You can write the equation as $$(bc)^n+(ac)^n=(ab)^n$$, so, it's impossible

- 2 years, 5 months ago

Thank you very much!

- 2 years, 5 months ago