Have a look here: Integer solutions for straight lines
I came across this..
here http://www.ams.org/journals/tran/194...-0006739-2.pdfIt 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.
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.