# 2. CONDITION

Do there exist two consecutive natural numbers, greater than 1000 000, such that the sums of their digits are perfect squares?
Solution. The desired numbers are, for example, $n=999999999$ and $\mathrm{n}+1=1000000000$, which have digit sums S(n) $=81, \mathrm{~S}(\mathrm{n}+1)=1$.

Answer: they exist.