We can repeat this process using the squares of $7$ and $4$ to get $65$ and then continue the process indefinitely.
Start with $145$ and see what happens.
Now we come to the most important step! Show that, whatever number we start with less than $1000$, we always get another number which is less than $1000$.
Choose some numbers less than $1000$ and, each time, repeat the process until you notice a pattern.
Make some conjectures about what happens in general.