As the title says I'm looking for a general solution to a Diophantine equation of the form:
$y^2 = x^2 + kx - m$
Where $x$ and $y$ are both positive integers. I know that $k$ and $m$ will always be a multiple of 2 if that helps.
Here are a few examples that I solved through brute force.
- $y^2 = x^2 + 30 x - 28$
$x = 2$
$y = 6$
- $y^2 = x^2 + 474 x - 554$
$x = 45$
$y = 151$
- $y^2 = x^2 + 1802 x - 3018$
$x = 37$
$y = 255$
I'm a bit of a dummy so a thorough explanation would be much appreciated. Thanks in advance!