Linear Diophantine Equation/Examples/15x + 51y = 41

Example of Linear Diophantine Equation
The linear diophantine equation:
 * $15 x + 51 y = 41$

has no solutions for $x$ and $y$ integers.

Proof
Using the Euclidean Algorithm:

Thus we have that:
 * $\gcd \set {15, 45} = 3$

which is not a divisor of $41$.

So, from Solution of Linear Diophantine Equation, no solution exists.