one could make the argument that this is a bit overkill
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lol i love this
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If I don't misremember this argument is circular, given that our only known proof of Fermat makes use of the fact that the roots of 2 are irrational (I heard that somewhere).
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If the big proof ever needed the fact that root is irrational, it didn't take that for granted but established it
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In a similar vein: I recently heard that a student in the BeNeLux Math olympiads proved 56 is not a cube by noting that 56=4³-2³ and then referring to Fermat's Last Theorem for n=3
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