MathNet 2025 — Part 01 (100 complete bilingual questions) Question 78

Determine the four-digit natural numbers $\overline{abcd}$, for which there exists a prime number $p$, such that $\overline{cd} - \overline{ab} = p + 2$ and $\sqrt{\overline{ab} - 4} + \sqrt{\overline{cd}} = p^2$.