1/x - 1/y = 1/2005

May 2005
39
0
Find all pairs of positive integers x and y that safisfy the equation:

1/x - 1/y = 1/2005
 
Apr 2005
103
1
x, y

1604, 8020

1980, 158796

2000, 802000

2004, 4018020
 
May 2005
39
0
Thanks Paul for finding the solutions!
 
Last edited:
May 2005
39
0
Hi there, i was wondering how you rearrange my first equation:

Namely: 1/x - 1/y = 1/2005

Into: y = -2005 + (2005^2/2005-x)

Thanks!
 
May 2005
39
0
Ok solved. No need to post an answer.

To solve add and subtract 2005^2 from the numerator... then it falls in place. Thanks anyway.
 
S

SbD

how can you prove it tho? how do you work it out?


x, y

1604, 8020

1980, 158796

2000, 802000

2004, 4018020

??
 
Aug 2005
24
0
Into: y = -2005 + (2005^2/2005-x)

Why is it like that?

Why isn't it y= -2005 + (2005^2/x-2005)