I have a Diophantine equation like this
10xy + 7y + 9x = 123456789..... (a 270 digit number!!)
I have tried an online calculator to solve it https://www.alpertron.com.ar/QUAD.HTM, but it is factoring that huge number, so it is taking a very very long time.
My question is : Is there any algorithm to solve Diophantine equations on this specific form
10xy + 7y + 9x = c
where c is a huge ~300 digits number, without the need for factorization?
I need a solution that doesn't take forever to calculate,
the only constraint is that x and y are integers
thanks.