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Algebra

Blazing goIITian

 Joined: 25 Jul 2011 Post: 322
25 Dec 2011 21:50:08 IST
4 People liked this
12
432
Divisibility probs...
Engineering Entrance , JEE Main , JEE Advanced , Mathematics , Algebra

find the no which when divided by 17 ,16,15 and the remainder is 3.10,0 respectively means u have to findthat no which is divided by 17 then it leaves the remainder3 when divided by 16 leaves remainder 10 and when divi ded by 15 leaves remainder 0

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
26 Dec 2011 10:57:32 IST
2 people liked this

use the chinese remainder theorem for this.

it is helpful in these types of questions.

we want to solve.

x = 0 (mod 15).

x = 3 (mod 17).

and x = 10 (mod 16).

a = b(modn) means that

(a-b) is divisible by n.

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
26 Dec 2011 11:09:29 IST
0 people liked this

hi,cme in gmail dude

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
26 Dec 2011 11:15:02 IST
0 people liked this

how to solve with mod??

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
26 Dec 2011 11:16:12 IST
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Can u pls gimme the link,so tat i can learn?

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
27 Dec 2011 10:21:07 IST
1 people liked this

well i will give you a link wait.////

http://www.math.nyu.edu/faculty/hausner/congruence.pdf

read this and let me know.

:-)

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
27 Dec 2011 11:14:29 IST
0 people liked this

Find 17^341 mod 5.This is an example of the pdf tat u gave......Can u explain it to me?....I cant get it....:-)

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
27 Dec 2011 13:55:26 IST
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How will u proceed the sum witha = b(modn) means that(a-b) is divisible by n.

Cool goIITian

Joined: 21 Jul 2010
Posts: 88
27 Dec 2011 19:07:43 IST
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?? ?????? ?? ??? ???? ?? ?? ???

Cool goIITian

Joined: 21 Jul 2010
Posts: 88
27 Dec 2011 19:08:42 IST
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3930 is the no. r8?

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
27 Dec 2011 19:18:19 IST
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yes,ps explain

Blazing goIITian

Joined: 27 Dec 2010
Posts: 1508
27 Dec 2011 20:24:31 IST
1 people liked this

after using the chinese remainder theorem i got the general solution to be

3930 + 4080k.

where k is a positive integer.

if you want i will post the full solution tomorrow.

Blazing goIITian

Joined: 25 Jul 2011
Posts: 322
27 Dec 2011 21:18:26 IST
0 people liked this

I need the solution,No probs,u can post it tommorow ;)

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