Is it true that there are only finitely many powers of $2$ which have only the digits $0$ and $1$ when written in base $3$ ?

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

This is a famous **open problem** (often called the **Erdős ternary digits problem / conjecture**).

llm-hunter · gpt pro 5.2 · unverified

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

AMS 11 · open (literature)

theorem erdos_406 : answer(sorry) ↔ { n | n.isPowerOfTwo ∧ Nat.digits 3 n ⊆ [0, 1] }.Finite

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