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How to find all solutions of Linear Diophantine Equation $a \cdot x + b \cdot y = c $ given $a,b,c$ where $c$ is divisible by $\gcd(a,b)$ and constraints are $x_0 \leq x \leq x_1$ and $y_0 \leq y \leq y_1$ ?

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  • $\begingroup$ Solution set of $(x,y,c)$ is every $x,y$ within the constraint, since every linear combination of $a,b$ is divisible by their GCD. $\endgroup$ – L KM Mar 29 at 10:03
  • $\begingroup$ @LKM. Given a = 1, b = c = 2, and 0 <= x,y <= 1000, how many integers x,y have x + 2y = 2??? $\endgroup$ – William Elliot Mar 30 at 2:22
  • $\begingroup$ Then of course there is 2 solutions, namely, $(x,y)=(0,1), (2,0)$. So the question should be formulated as follows? \\ How to find all solutions (x,y) of Linear Diophantine Equation $a \cdot x + b \cdot y = c$ with $a,b,c$ fixed and c divisible by $\gcd(a,b)$ ? $\endgroup$ – L KM Mar 30 at 4:10
  • $\begingroup$ Edited the question. $\endgroup$ – Parth Patel Mar 30 at 13:45

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