Problem 2

We say that a 4-digit year is square-loving if splitting it "in the middle" into two 2-digit numbers, summing these and squaring the result, we arrive at the year we started with. For example, $2025$ splits into $20$ and $25$, and $(20 + 25)^2 = 2025$ so $2025$ is square-loving. The next square-loving year is $3025 = (30 + 25)^2$. What is the next square-loving year after $3025$?

To deter guessing without thinking, we ask that you also solve the following simple arithmetic problem before checking your answer:

What is 2 + 7 - 4?

This problem was first solved on Wed 22nd January at 4:02:58pm