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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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8  
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
1  
@Leandro: There do not exist such integers, right? –  Gigili Jan 30 '12 at 15:46
1  
@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
2  
(+1) for work shown in comments! –  The Chaz 2.0 Jan 30 '12 at 16:29

1 Answer 1

up vote 8 down vote accepted

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 $z$ .

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