Use Fermat-Kraitchik’s factorization to factor $85026567$
Solution 1:
This method works quickly when the factors are close together. In this case, the factors are very far apart, so the associated $t_i$ will be huge.
Remember why this method works: $x^2-n=y^2$ means $n=x^2-y^2=(x-y)(x+y)$. In this example, we want to "discover" this factorization when $x-y=3$ and $x+y=28342189$, which means that $x=14171096$ and $y=14171093$. So this method won't find the factorization until $t_i=14171096$!