## number theory problem

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tushar7
Posts: 101
Joined: Tue Dec 07, 2010 3:23 pm

### number theory problem

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

AntiviruShahriar
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
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### Re: number theory problem

viivviiave
Posts: 4
Joined: Sat Dec 25, 2010 7:25 pm

### Re: number theory problem

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

tushar7
Posts: 101
Joined: Tue Dec 07, 2010 3:23 pm

### Re: number theory problem

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
Posts: 125
Joined: Mon Dec 13, 2010 12:05 pm
Location: চট্রগ্রাম,Chittagong
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### Re: number theory problem

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
Posts: 4
Joined: Sat Dec 25, 2010 7:25 pm

### Re: number theory problem

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
Posts: 158
Joined: Wed Dec 08, 2010 5:36 pm

### Re: number theory problem

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

tushar7
Posts: 101
Joined: Tue Dec 07, 2010 3:23 pm

### Re: number theory problem

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

leonardo shawon
Posts: 169
Joined: Sat Jan 01, 2011 4:59 pm
Location: Dhaka

### Re: number theory problem

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

long way to go .....

HandaramTheGreat
Posts: 135
Joined: Thu Dec 09, 2010 12:10 pm

### Re: number theory problem

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