Let $n=pq$, where $p=13710221545914561761$ and $q=11066328760152681859$ are both primes. Find the (two) square roots of $1\bmod n$ that are $\ne\pm1\bmod n$. Let the square roots be $a_1\bmod n$ and $a_2\bmod n$, with $a_1,a_2\in\{0,\dots,n-1\}$, and $a_1>a_2$, find $a_1$.
The problem is related to modular arithmetic involving prime numbers.