Find the least positive integer $k$ so that $k + 25973$ is a palindrome (a number which reads the same forward and backwards).
1. To find the least positive integer \( k \) such that \( k + 25973 \) is a palindrome, we need to identify the smallest palindrome greater than 25973.
2. A palindrome is a number that reads the same forward and backward. We start by examining numbers greater than 25973 to find the next palindrome.
3. We check the number 25974, 25975, and so on, until we find a number that is a palindrome.
4. By inspection, we find that the number 26062 is the next palindrome after 25973.

   \[
   26062 \text{ is a palindrome because it reads the same forward and backward.}
   \]

5. Now, we calculate \( k \) by finding the difference between 26062 and 25973:

   \[
   k = 26062 - 25973
   \]

6. Performing the subtraction:

   \[
   k = 26062 - 25973 = 89
   \]

Therefore, the least positive integer \( k \) such that \( k + 25973 \) is a palindrome is 89.

The final answer is \( \boxed{89} \)