BdMO Online Forum

Writing down all the integers from $1$ to $100$ we make a large integer $N$.
$N=123456789101112...9899100$.
What will be the remainder if we divide $N$ by $3$?

Answer:$\fbox 1$
Summation of $3$ consequetive intergers is always divided by $3$.
So,$N\equiv 1(mod 3)$.