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import FormalConjecturesUtilErdős Problem 249
open scoped Nat
namespace Erdos249
Is $$\sum_{n} \frac{\phi(n)}{2^n}$$ irrational? Here $\phi$ is the Euler totient function.
@[category research open, AMS 11]
theorem erdos_249 : answer(sorry) ↔ Irrational (∑' n : ℕ, (φ n) / (2 ^ n)) := ⊢ True ↔ Irrational (∑' (n : ℕ), ↑(φ n) / 2 ^ n)
All goals completed! 🐙
end Erdos249