We're given a number $n\in [10^9,10^{10}]$ and its smallest prime factor $p$. Then we are asked to find $p - 1$ numbers with $a^{p-1} \equiv 1\bmod n$, and some other number of numbers which are not.

We did this by just rerunning until $p = 3$, using Sage:
```
K = Integers(11081914353)
r = K(1)
print(r.nth_root(3, all=True))

> [1, 7429528459, 7346357344, 3693971452, 41585557, 11040328795, 7387942903, 3735557008, 3652385893]
```

And then submitting these, interspersing with small numbers which when cubed can never be 1 modulo $n$ (such as 2 or 3).

Given the pattern `001100`, we can do:
```
001100
Enter: 2 3 7429528459 7346357344 4 5
b'flag{pr1mes_r_pr3tty_sp3c14lll}'
```