We say that $a, b \in N$ are an amicable pair if $σ (a) = σ (b) = a + b$ . Are there infinitely many amicable pairs? If $A (x)$ counts the number of amicable $1 \leq a \leq b \leq x$ then is it true that $A (x) > x^{1 - o (1)} ?$

unreviewedOpen. Worked here; no verified result yet.

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

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Evidence

unverified AI candidates (2)

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

No proof is known that there are infinitely many amicable pairs.

llm-hunter · gpt pro 5.2 · unverified

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

Formal proof

AMS 11 · open (literature)

theorem erdos_830.parts.i : answer(sorry) ↔ {(a, b) | IsAmicable a b}.Infinite

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