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number theory problem

Posted: Fri Dec 24, 2010 1:25 am
by tushar7
Find the remainder when $1!+2!+3!....+99!$ is divided by $30$.

Re: number theory problem

Posted: Fri Dec 24, 2010 11:32 am
by AntiviruShahriar
$6!$ থেকে বড় শংখ্যার factorial গুলো $30$ দ্বারা বিভাজ্য।
অর্থাৎ, $1!+2!+3!+4!+5!$ $\equiv$ $3$ (mod 30)
ans: $3$.......

Re: number theory problem

Posted: Sat Dec 25, 2010 8:08 pm
by viivviiave
wait
i don't understand. both 5! and 6! are also divisible by 30

Re: number theory problem

Posted: Sat Dec 25, 2010 9:42 pm
by tushar7
viivviiave wrote:wait
i don't understand. both 5! and 6! are also divisible by 30
i did not get what you meant ....but explaing a liitle bit

you can clearly see $6!=1.2.3.4.5.6$ so its clearly divisible by 30 and from 6! any 'integer factorial' would be divisible by 30 . so we just need to think about $1!$ to $5!$ and i you are right that $5!$ is divisible by 30

Re: number theory problem

Posted: Mon Dec 27, 2010 11:24 am
by AntiviruShahriar
viivviiave wrote:wait
i don't understand. both 5! and 6! are also divisible by 30
yup i did'nt think about $5!$......it was my mistake but as $a$ $\equiv$ $a+n$ $(mod n)$, $5!$ can't change the ans.

Re: number theory problem

Posted: Tue Dec 28, 2010 6:38 pm
by viivviiave
AntiviruShahriar wrote:
viivviiave wrote:wait
i don't understand. both 5! and 6! are also divisible by 30
yup i did'nt think about $5!$......it was my mistake but as $a$ $\equiv$ $a+n$ $(mod n)$, $5!$ can't change the ans.
yup!!!

Re: number theory problem

Posted: Wed Dec 29, 2010 12:42 pm
by Dipan
I can't understand the question...if the given series is divided by 30 how can we get remainder????/

Re: number theory problem

Posted: Wed Dec 29, 2010 1:30 pm
by tushar7
from $5!$ to $99!$ is divisible bt 30 .

Re: number theory problem

Posted: Thu Jan 20, 2011 3:32 am
by leonardo shawon
Then 1! 2! 3! 4! ?? That mean 288?

Re: number theory problem

Posted: Thu Jan 20, 2011 11:20 am
by HandaramTheGreat
leonardo shawon wrote:Then 1! 2! 3! 4! ?? That mean 288?
you've multiplied them... was the question like that? ;)