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Unusual Equation Problem (Posted on 2006-11-28)

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
no programming	Larry	2006-11-28 16:07:15
solution	Charlie	2006-11-28 10:37:49

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