Thread: integer solutions for a straight line

Hi,

I came across this..

It is well known that the equation Ix + my + n = 0, with rational integral coefficients, has either no solution in rational integers
or an infinite number of solutions.

here http://www.ams.org/journals/tran/194...-0006739-2.pdf

How is it possible to determine whether a straight line has rational integer solutions or not?

has integer solutions at (11, 25), (29, 65), (199, 445)......

It appears that there are no integer solutions for but I don't know how to go about proving (or disproving) there are no integer solutions.

I'd be grateful if someone could provide any help.

Thanks

Have a look here: Integer solutions for straight lines

Originally Posted by earboth

Have a look here: Integer solutions for straight lines

Thanks earboth, I'll take a peek at my post in a while

btw, there are two corrections to my OP

1) hyperbola, not straight line

2) x and y must be coprime

thanks again