Heloo again, yuriythebest!
The second problem is rather bizarre.
I will assume we want integer solutions.
I found no direct approach to it . . .
We have: .
Divide by 10: .
The left side is of the form: .
The right side is of the form: .
They are equal only when: .
As usual, Soroban, your post is very useful. However, the left side of your equation is never actually 1. The highlighted element should be .
So, we really have
Of course, you still had the right solution.
Incidentally, the other solution should be about , determined by Newton's method.