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Fermat's Last Theorem Variation

The attached question is a variation on Fermat's Last Theorem.

I would be grateful to anyone able to solve the problem.

I would be grateful to anyone able to answer and prove the answer to the following question:

If a, b, c and n are rational numbers, but they are not integers, do there always exist a, b, c and n such that for n > 2?

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The proof to this problem is by no means an easy solution. I did some ...

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