In the book [Lectures on modular forms](http://books.google.com.tw/books/about/Lectures_on_modular_forms.html?id=UBwjJAiMZtcC&redir_esc=y), one finds the statement at page 8 that 

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> If $(a,b,c)=1$ then there is $n\in \mathbb Z$ such that $(a,b+nc)=1$. 
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I know that, if $(a,b)=1$, then we can take $n=0$. But, if $(a,b)\not=1$, then what could we do? Further, I tried to look at the linear combinations of $a, b, c$ which are $=1$, but to no avail have I discovered anything. The main difficulty I encountered is that the coefficient of $b$ might not be $1$.  

Any hint is well-appreciated.  

Thanks in advance.