Problem 44788. Find the right number make the equation

Interesting. I've solved several more puzzles in the Community group after this one, but I still can't see your solution, Binbin. It's obviously much smaller than mine is, which is why I'm interested in figuring out how you did this.

@ James
To unlock all solutions of this problem, you must solve a newer problem than this one, not older problems.

@James, my solution is very simple, it is pure number.The challenge is from Fermat. Because the big number, it is hard to test. I want use Java's Big Integer, but it has no sqrt operation.

My program gives a wrong answer for n=1, but passes the tests due to insufficient precision. How big is the smallest solution for n=1?

@Tim, it is about 13 digitals. I want to submit another problem use char array as output and avoid to precision.

@James, @Tim, Because of precision, the problem have no meaning, so I have fix the test suits. The output must be char array. Thank you for your support.