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The basis for Fermat's Last Theorem was Pythagoras's theorem. The latter showed that in any right angled triangle, the lengths of the sides satisfies

a^2 + b^2 = c^2.

In particular, that there are integer solutions to the equation: such as {3, 4, 5} or {5, 12, 13}.

Fermat's theorem proved that there were no non-trivial solutions for

a^n + b^n = c^n for any positive integers a, b, c and n where n > 2

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Q: What is the basic of Fermat's last Theorem?
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