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

Home > Just Math
Divisibility by 7 (Posted on 2005-05-22) Difficulty: 2 of 5
(2222^5555 + 5555^2222) is or isn't divisible by 7 ?

Just pencil and paper.

See The Solution Submitted by pcbouhid    
Rating: 2.0000 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Alternative Methodology Comment 8 of 8 |

We observe that:

2222(Mod 7) = 3, and:
5555(Mod 7) = 4

Thus,

(2222^5555 + 5555^2222)(Mod 7)
=(3^5555 + 4^2222)(Mod 7)
= ((3^5)^1111 + (4^2)^1111)(Mod 7)
= (243^1111 + 16^1111) (Mod 7)
= ((-2)^1111 + 2^1111) (Mod 7)
= (-2^1111 + 2^1111) (Mod 7)
= 0

Consequently, (2222^5555 + 5555^2222) is divisible by 7

Edited on November 14, 2007, 4:13 am
  Posted by K Sengupta on 2007-11-14 04:12:54

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 (4)
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