Some time ago I happened to see a proof that was remarkable in that it used both the Riemann Hypothesis and its negation. That is, it considered the two cases: RH is true, and RH is false, obtaining, after a non-trivial chain of reasoning in each case, the theorem in question. I failed to bookmark it well enough that I can readily retrieve it, so I’m asking the community’s help.
What reminded me of this result was this question on MO about famous vacuously true statements. Obviously, one of the cases in the proof is vacuous and, since it involves the Riemann Hypothesis, conceivably qualifies as being famous.
Answer
There is a small list on Wikipedia: https://en.wikipedia.org/wiki/Riemann_hypothesis#Excluded_middle
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