Lets say I have a diophantine equation ,
aX - bY = c
Now, for some (a,b,c) I may not have any integer solution at all. But lets say , I write the equation in this way ,
aX - bY = c + p
p is an integer . (positive or negative)
So, I can increase the value of c by (c+p) if there are no solution for (a,b,c). I need to find a triplet (a,b,c+p) for which solution exist and p is minimum(absolute value).
If , already I have solution for (a,b,c) then p is just 0.
How to solve this problem ?