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Solving a question using Chinese remainder theorem`
by IIM Calling!!!! - Sunday, 15 June 2008, 07:02 PM
 

Hey Guys,

If somebody is aware of the Chinese theorem, please try and solve this problem using the same:

Remainder when 123.... repeated 300 times is divided by 99?

By the Chinese theorem my answer is coming as 330 whereas the actual answer is 33.. please suggest what is the mistake happening.. Do I need to consider smaller roots of 9x + 11y = 1?? 

Re: Solving a question using Chinese remainder theorem`
by Bhaaai Boloooo - Thursday, 19 June 2008, 09:58 AM
 

Hi Nakul,

if you have got a remainder of 330 after all the calculation, do remember that it is still divisible by 99. If you divide 330 by 99 you will 33 as the remainder.

Can you explain the chinese theorem?

Thanks

 

Suresh

Re: Solving a question using Chinese remainder theorem`
by Rajesh Yadav - Monday, 23 June 2008, 02:06 PM
 

I think Ques. should be like this

123123...... 300 digits

(a) This no. is divisible by 11

(b) for divisibility by 9 = 3*100(3 digit is appearing 100 times) + 2*100+1*100

= 600

600 will give 6 Rem when divided by 9

So as per Chinese Them. 11x = 9y+6

So the smallest no is 33, which is divisible by 11 and gives 6 rem when/9. hope it is clear.

If Ques is same as provided by u, then

123123......... 300 times

(1) this no is divisible by 11

(2) 3*300 + 2*300 + 1*300 = 1800 which is also divisible by 9

so Ans is 0 (no rem.)

Hope you are clear now.

Re: Solving a question using Chinese remainder theorem`
by Abhijit Tambe - Tuesday, 6 September 2011, 03:47 AM
  Nice Solution......but some addition is required in the later part

divisible by 11 -----correct
divisible by 9-------correct
+ hence it is divisible by 99 giving remainder 0 only because 11 and 9 are co-prime numbers.

Re: Solving a question using Chinese remainder theorem`
by harsh goel - Monday, 6 February 2012, 09:56 AM
  gr8 comment man...