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

Home > Just Math
Unusual Equation Problem (Posted on 2006-11-28) Difficulty: 2 of 5
Let us denote by [x] the greatest integer ≤ x.

How many positive integers p satisfy [p/95]=[p/97]?

How many positive integers q satisfy [q/2005]=[q/2007]?

  Submitted by K Sengupta    
Rating: 5.0000 (1 votes)
Solution: (Hide)
PART A:

Both sides of the equation yield:

0, when p = 1 to 94.
1, when p = 97 to 189,
---------------------------
----------------------------
47 , when p = 4559

Hence, required number of positive integers p
= (1+3+5+-----+ 95) - 1
= 48^2 -1
= 2303.

PART B:

Both sides of the equation yield:

0, when q = 1 to 2004.
1, when q = 2007 to 4009,
---------------------------
----------------------------
1002 , when q = 2011014

Hence, required number of positive integers q
= (1+3+5+-----+ 2005) - 1
= 1003^2 -1
= 1006008

Comments: ( You must be logged in to post comments.)
  Subject Author Date
Solutionno programmingLarry2006-11-28 16:07:15
SolutionsolutionCharlie2006-11-28 10:37:49
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 (14)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2024 by Animus Pactum Consulting. All rights reserved. Privacy Information