While working on my integer factorization project, I came to this:
$(A + CX)(B + CY) = D$
- $X,Y,A,B,C,D$ Are integer numbers
- $A,B,C,D > 0$
- $X,Y >= 0$
- $A,B,X,Y < C < D$
- If $X=Y$ than $Y > 0$ to avoid trivial solutions where $X = Y = 0$
What assignment of $A,B,C,D$ will provide only one solution for $X,Y$?
It looks like Diophantine equation can be handy here. But I do not know how to apply it.
I am not looking for example but for patterns.
Here is an example for such case:
$A=7;B=3;C=10;D=391$
$(7 + 10X)(3 + 10Y)=391$
The only solution here is: $X=1;Y=2$
For $D$ arbitrary, let $A=1$, $B=1$, $C=D-1$. Then the only solution is $X=0$, $Y=1$.