number theory problem

Forum rules
Please don't post problems (by starting a topic) in the "X: Solved" forums. Those forums are only for showcasing the problems for the convenience of the users. You can always post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.
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
Contact:

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
Contact:

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?