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I have no idea what to do about this question:

Are there integers like $x$, $y$ and $z$ that

$6x+9y+15z=107$

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    @AndreaMori: Great, now I know what is the theorem called. Thank you.2012-01-30

1 Answers 1

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Since $3 \mid 6$ and $3 \mid 9$ and $3\mid 15$, $3$ should divide the right hand side but $ 3\nmid 107$. Hence there do not exist such integers $x$, $y$ and $z$ .