All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Evaluate this remainder (Posted on 2008-08-13) Difficulty: 2 of 5
What is the remainder when you divide 299 by 99?

See The Solution Submitted by pcbouhid    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Alternative Methodology | Comment 4 of 6 |
(In reply to Solution by K Sengupta)


Alternatively, expanding by Binomial Theorem, we have:

2^95
= (33-1)^19
= (33^19 comb(19, 1)*33^18 +......- comb(19,17)*33^2 +  comb(19,18)*33 1)
= M(99) + 19*33 -1,
= M(99) +  18*33 + (33-1)
= M(99) + 32

Accordingly,

2^95 (mod 99) = 32, so that:
2^99 (mod 99) = (32*16) mod 99

But, 32*16
= (33-1)(15+1)
 = 33*15 +(33-15-1)
= M(99) + 17, since 15 is divisible by 3, so that 33*15 is divisible by 99

Accordingly, 
2^99 (mod 99) = 17

Consequently, the required remainder is 17.


  Posted by K Sengupta on 2008-08-13 11:38:11
Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (9)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2017 by Animus Pactum Consulting. All rights reserved. Privacy Information