Competition problem — Number theory

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Number theory Difficulty 5.5 AIME, harder Find the answer

Inference 1 Let $b \geqslant 3$ be a natural number, $(b, 10)=1$ , and the order of 10 modulo $b$ be $t_{0}$ , then among
$\frac{1}{b}, \frac{2}{b}, \cdots, \frac{b-1}{b}$

there are exactly $t_{0}$ fractions whose repeating decimals consist of the same $t_{0}$ digits in cyclic permutations.

Your answer

A number or a short expression. Spacing and $ signs are ignored.

Solution

None

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Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic and difficulty added by this site.