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

Find all pairs of positive integers x and y that safisfy the equation:

1/x - 1/y = 1/2005

x, y

1604, 8020

1980, 158796

2000, 802000

2004, 4018020

Thanks Paul for finding the solutions!

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!

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.

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


x, y

1604, 8020

1980, 158796

2000, 802000

2004, 4018020

??

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

Why is it like that?

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