Recently, I came across a post on MO that asked for complicated proofs of trivial statements. The highest voted answer was :

Theorem: $2^{\frac{1}{n}}$ is irrational for $n > 2$.

Proof: Assume the contrary, say $2^{\frac{1}{n}} = \frac{x}{y}$. Then, $x^n = 2 y^n = y^n + y^n$ contradicting Fermat’s Last Theorem.

Remark: Unfortunately, FLT can’t prove the irrationality of $\sqrt 2$!

Tailpiece: I recently made a (just working) webpage on my institute website. Here is its link.

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