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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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    Hint: $3$ divides the left handed side, which equals the right handed side..2012-01-30
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    @Leandro: But $3$ doesn't divide the right handed side.2012-01-30
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    So...? conclusion?2012-01-30
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    @Gigili: my point exactly. What does that tell us?2012-01-30
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    @Leandro: There do not exist such integers, right?2012-01-30
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    @Gigili: absolutely.2012-01-30
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    @Gigili: you're welcome. :) By the way, it's often a good idea to look at divisors when trying to solve questions like this.2012-01-30
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    @Gigili: You can write it yourself! Write down a proof that no solutions exist; people can help you with suggestions (if needed) and you can eventually accept it.2012-01-30
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    It may be of some help to check this: http://en.wikipedia.org/wiki/B%C3%A9zout%27s_identity2012-01-30
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    @AndreaMori: Great, now I know what is the theorem called. Thank you.2012-01-30

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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 $z$ .