Goldbach's proof of the infinitude of primes.
As a warm-up to Euler's proof that the primes are infinite, I present Goldbach's proof, which seems to be not so well known. It should be, though, because it's a beautiful and fascinating proof. Goldbach uses peculiar properties of Fermat numbers in a way that is quite thought-provoking. Mathematical Induction playlist... • Dirichlet kernel sum and other application...
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