One example are the repunits where $a=1$, $b=1$, and $c=9$. Another example are the numbers of the form 133...331 which are generated by the values $a=4$, $b=7$, and $c=3$. There are lots of other examples. Is there a way to determine for a given value of $a$ which values are always guaranteed to return an integer?
2026-02-23 08:33:06.1771835586
For a given $a$, for which values of $b$ and $c$ is the sequence $\frac{a\cdot10^n-b}{c}$ guaranteed to return integer terms with GCD=1?
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