Linear Diophantine Equation/Examples/15x + 27y = 1

Example of Linear Diophantine Equation
The linear diophantine equation:
 * $15 x + 27 y = 1$

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

Proof
We have that:
 * $\gcd \set {15, 27} = 3 \nmid 1$

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