## BdMO National Secondary 2007#2

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### BdMO National Secondary 2007#2

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 $3$?

samiul_samin
Posts: 1007
Joined: Sat Dec 09, 2017 1:32 pm

### Re: BdMO National Secondary 2007#2

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