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

Home > Numbers
Getting the right count (Posted on 2015-07-14) Difficulty: 2 of 5
Find the total number of positive integers n not over 2015 such that n^4+5n^2+9 is divisible by 5.

Source: SMO, slightly modified

No Solution Yet Submitted by Ady TZIDON    
Rating: 3.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution Analytical Solution Comment 1 of 1
Well, we can ignore the 5n^2 term, which is always divisible by 5.
All we need is n^4 = 1 mod 5.

1^4 = 1 mod 5
2^4 = 16 = 1 mod 5
3^4 = 81 = 1 mod 5
4^4 = (2^4)^2 = 1 mod 5
5^4 = 0 mod 5

so this works for 4/5 of all integers.

Answer = 2015 * 4/5 = 1612

  Posted by Steve Herman on 2015-07-14 10:05:06
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 (3)
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