Question 83
An integer $n \gt 1$ will be called *p-periodic* if $\frac{1}{n}$ is a repeating decimal fraction, whose shortest period has length $p$ and begins immediately after the decimal point. For instance, $\frac{1}{9} = 0.111\dots$ is 1-periodic and $\frac{1}{11} = 0.090909\dots$ is 2-periodic.
a) Find all p-periodic numbers $n$ so that the first digit of the period of $\frac{1}{n}$ is not nil.
b) Find the largest 4-periodic prime.
a) Find all p-periodic numbers $n$ so that the first digit of the period of $\frac{1}{n}$ is not nil.
b) Find the largest 4-periodic prime.