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

## Example of Linear Diophantine Equation

$15 x + 27 y = 1$

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

## Proof

We have that:

$\gcd \set {15, 27} = 3$

which is not a divisor of $1$.

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

$\blacksquare$