# Does the Diophantine Equation 378x + 222y = 8

Does the Diophantine Equation378x + 222y = 8
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nick1337

We have to determine whether following diophantine equation has solution

Recall that diophantine equation $ax+by=c$ has solution if g.c.d.$\left(a,b\right)$ divides $c$

$\circ$ g.c.d.$\left(a,b\right)$ $=$greatest common divisor of

Compare  with $ax+by=c$

we get

Here, g.c.d$\left(378,222\right)=6$

Which is not divide $8$

$\therefore$ By the above result diophantine equation  has no sultion