Is it true that, for any $a \in Z$ , there are infinitely many $n$ such that $ϕ (n) ∣ n + a ?$

Worked, still open.

number theory · open · formalized (Lean) · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

evidence

unverified AI candidates (2)

gpt-erdos · GPT-5.2 Pro + Deep Research · unverified

No one currently knows how to prove (or disprove) that this holds **for every** integer $a$.

llm-hunter · gpt pro 5.2 · unverified

1 LLM attack(s) recorded (gpt pro 5.2); unverified.

AMS 11 · open (literature)

theorem erdos_828 : answer(sorry) ↔ ∀ a : ℤ, Set.Infinite {n : ℕ | ↑(φ n) ∣ n + a}

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