Project Euler Problem 719
We define an S-number to be a natural number, n, that is a perfect square and its square root can be obtained by splitti
Solution
Answer: 128088830547982
Using a correct search over all square roots $r \le 10^6$ (since $r^2 \le 10^{12}$), checking whether the decimal representation of $r^2$ can be split into two or more contiguous parts summing to $r$, and applying the necessary congruence filter $r^2 \equiv r \pmod 9$ (so $r \equiv 0,1 \pmod 9$) for efficiency, we reproduce the given check:
$$T(10^4)=41333$$
which matches the problem statement.
Running the full computation up to $10^{12}$ gives:
Answer: 128088830547982