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The mathematical community is now aware beyond reasonable doubt that Fermat's Last Theorem was accurate. However, I cannot help asking, if there were any non trivial Fermat's triplet:

-What would have been the form of those integers?

-Would $x,y,z$ have the same form as $x^n,y^n,z^n$? For instance, Pythagoras's triplets are all the difference or the sum of 2 squares $$x=p^2-q^2$$ $$y=(\dfrac{p+q}{\sqrt 2})^2-(\dfrac{p-q}{\sqrt 2})^2$$

$$z=p^2+q^2$$ Which is strikingly similar to the square of those integers: $$x^2=z^2-y^2$$ $$y^2=z^2-x^2$$ $$z^2=x^2+y^2$$ What are your thoughts?

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    $\begingroup$ Prior to Andrew Wiles, there were many partial results in the preceding centuries. A historical search would be needed. $\endgroup$ – DanielWainfleet May 3 '16 at 21:37
  • $\begingroup$ I am not looking for a proof. Wiles provided us with one. I am looking for a probable form of those integers. $\endgroup$ – user97615 May 3 '16 at 21:41

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