BdMO National Secondary 2007#2

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samiul_samin
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BdMO National Secondary 2007#2

Unread post by samiul_samin » Sat Feb 23, 2019 11:05 am

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 $3$?

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samiul_samin
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Re: BdMO National Secondary 2007#2

Unread post by samiul_samin » Sat Feb 23, 2019 11:10 am

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

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