Fermat's right triangle theorem (https://en.wikipedia.org/wiki/Fermat%27s_right_triangle_theorem#Fermat%27s_proof), now a Good Article on Wikipedia.
As Fibonacci observed and Fermat proved (as his only surviving proof), integer right triangles cannot have an area that is a perfect square. One corollary of this is the exponent-4 case of Fermat's Last Theorem.
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