I have written a Python program running over $i$, but up to billions there is no solution, so I guess there is no solution. Trying to prove that, I looked at multiplicative order, but I do not get a grip on $9i +1$. Anybody an idea for the proof (or finding a huge $i$)?
2026-02-23 09:30:22.1771839022
Find a positive integer $i$ such that $9i + 1$ divides $2 \times 10^i - 1$
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