# Math Help - GCD equation question

1. ## GCD equation question

The following question was confusing me so any help would be appreciated!

Find the solution in integers to the equation
155x+341y+385z=1 (where 1 is the gcd of 155,341, and 385).

2. Originally Posted by clockingly
The following question was confusing me so any help would be appreciated!

Find the solution in integers to the equation
155x+341y+385z=1 (where 1 is the gcd of 155,341, and 385).
Okay, rewrite this equation as,
$155x+341y = 1 - 385 z \ \ \ (1)$.
Now $\gcd(155,341)=31$ this means (1) has a solution whenever $31 | (1-385z)$, i.e. $385z\equiv 1 (\bmod 35)$.
But this congruence has no solution to it because $385 \equiv 0$ under this modulos. Thus, this equation has no solutions.