# Two Sets: Necessary Condition for Solution \[ \sum_{k=1}^n k = \frac{n(n + 1)}{2}. \] Let the sum of integers in each of the two result sets be \( s \). Thus \( 2s = n(n + 1)/2 \). Therefore \[ s = \frac{n(n + 1)}{4}. \] Since \( s \) is sum of integers, \( s \) must be integer. Therefore \[ n(n + 1) \equiv 0 \pmod{4}, \] or \[ n \equiv 0 \text{ or } 3 \pmod{4}. \]