BdMO National Junior 2010/4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
samiul_samin
Posts:1007
Joined:Sat Dec 09, 2017 1:32 pm
BdMO National Junior 2010/4

Unread post by samiul_samin » Sun Feb 24, 2019 9:33 am

Find the smallest number,divisible by $13$ ,such that the remainder is $1$ when divided by $4,6$ or $9$.

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

Re: BdMO National Junior 2010/4

Unread post by samiul_samin » Mon Feb 25, 2019 11:46 am

Answer:$\fbox {325}$

Solution:
LCM$(4,6,9)=36$
So the number must be $36n+1$
and the number can also be presented as $13m$
That means $36n+1=13m$
Where $n$,$m$ both are integers.
Pluuging the value of $n$ from $1$ to $9$ .
We will get our desired answer $325$.

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