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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 \(n>2\).

Note: If this question was already asked please show me the link of that discussion so I can look over that.

If this is possible tell me why it is possible.

If this is impossible tell me why it is impossible.

Note by Ananth Jayadev
1 year, 11 months ago

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

Otto Bretscher - 1 year, 11 months ago

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Thank you very much!

Ananth Jayadev - 1 year, 11 months ago

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