Are there infinitely many $n$ such that there exists some $t \geq 2$ and distinct integers $a_{1}, \dots, a_{t} \geq 1$ such that $\frac{n}{2 ^{n}} = 1 \leq k \leq t \sum \frac{a _{k}}{2 ^{a_{k}}} ?$ Is this true for all $n$ ? Is there a rational $x$ such that $x = k = 1 \sum \infty \frac{a _{k}}{2 ^{a_{k}}}$ has at least $2^{ℵ_{0}}$ solutions?

Worked, still open.

number theory · open · 0 attempts

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vela registry pull vfr_37aec80d874a0239

vela reproduce examples/erdos-problems

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unverified AI candidates (2)

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

## 1) Infinitely many $n$ in the finite-sum equation

llm-hunter · gpt pro 5.2 · unverified

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

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