2022-03-11
Answered

Does the Diophantine Equation378x + 222y = 8

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nick1337

Answered 2022-03-21
Author has **510** answers

We have to determine whether following diophantine equation has solution

$378x+222y=8$

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

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

Compare $378x+222y=8$ with $ax+by=c$

we get $a=378,b=222c=8$

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

Which is not divide $8$

$\therefore $ By the above result diophantine equation $378x+222y=8$ has no sultion

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