How did I not know this? The decimal expansion of 2017 repeats every 2016 digits!

@christianp Looking through the list, it often seems to be the case that the number of repeated digits is either $n-1$ or $\frac{n-1}{2}$. I’m sure there’s a theorem to be proved here (and I’m sure someone has already done so).

@skalyan @christianp I think it has to do with the multiplication group of non-zero integers mod n. The size of the group is n-1, so the cycles are going to be factors of that, and the decimal repeats based on the cycle generated by 10?

A Mastodon instance for maths people. The kind of people who make $\pi z^2 \times a$ jokes.

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