Does the Diophantine Equation 378x + 222y = 8

2022-03-11 Answered
Does the Diophantine Equation378x + 222y = 8
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Answers (1)

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

 g.c.d.(a,b) =greatest common divisor of a & b

Compare 378x + 222y = 8 with ax+by=c

we get a=378, b=222 & c=8

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

Which is not divide 8

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

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