A4. Any natural number of two digits can be written in reverse. So you can reverse 15 to 51. There are two-digit numbers with the property that the number added to its reverse results in a number that is the square of an integer.

Determine all numbers with this property.
A4. Write a two-digit number as $\overline{a b}=10 a+b$. Then $\overline{a b}+\overline{b a}=11(a+b)$. Therefore, $11(a+b)$ must be a square. This means that $(a+b)$ is equal to 11 or equal to a square times 11. The latter is not possible because $(a+b)$ cannot be as large as 44. What remains is $(a+b)=11$ with the solutions: 29, 38, 47, 56, 65, 74, 83 and 92.