# Are there integers like $x$, $y$ and $z$ that $6x+9y+15z=107$?

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.. – student Jan 30 '12 at 15:38
@Leandro: But $3$ doesn't divide the right handed side. – Gigili Jan 30 '12 at 15:40
@Leandro: There do not exist such integers, right? – Gigili Jan 30 '12 at 15:46
@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. – Arturo Magidin Jan 30 '12 at 16:15
(+1) for work shown in comments! – The Chaz 2.0 Jan 30 '12 at 16:29

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 $z$ .