number theory problem

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tushar7
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number theory problem

Unread post by tushar7 » Fri Dec 24, 2010 1:25 am

Find the remainder when $1!+2!+3!....+99!$ is divided by $30$.

AntiviruShahriar
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Re: number theory problem

Unread post by AntiviruShahriar » Fri Dec 24, 2010 11:32 am

$6!$ থেকে বড় শংখ্যার factorial গুলো $30$ দ্বারা বিভাজ্য।
অর্থাৎ, $1!+2!+3!+4!+5!$ $\equiv$ $3$ (mod 30)
ans: $3$.......

viivviiave
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Re: number theory problem

Unread post by viivviiave » Sat Dec 25, 2010 8:08 pm

wait
i don't understand. both 5! and 6! are also divisible by 30

tushar7
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Re: number theory problem

Unread post by tushar7 » Sat Dec 25, 2010 9:42 pm

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

AntiviruShahriar
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Re: number theory problem

Unread post by AntiviruShahriar » Mon Dec 27, 2010 11:24 am

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.

viivviiave
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Re: number theory problem

Unread post by viivviiave » Tue Dec 28, 2010 6:38 pm

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!!!

Dipan
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Re: number theory problem

Unread post by Dipan » Wed Dec 29, 2010 12:42 pm

I can't understand the question...if the given series is divided by 30 how can we get remainder????/

tushar7
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Re: number theory problem

Unread post by tushar7 » Wed Dec 29, 2010 1:30 pm

from $5!$ to $99!$ is divisible bt 30 .

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leonardo shawon
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Re: number theory problem

Unread post by leonardo shawon » Thu Jan 20, 2011 3:32 am

Then 1! 2! 3! 4! ?? That mean 288?
Ibtehaz Shawon
BRAC University.

long way to go .....

HandaramTheGreat
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Re: number theory problem

Unread post by HandaramTheGreat » Thu Jan 20, 2011 11:20 am

leonardo shawon wrote:Then 1! 2! 3! 4! ?? That mean 288?
you've multiplied them... was the question like that? ;)

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