# A number theory problem by Kian Chua

Number Theory Level 3

Consider positive integers solutions $$(x,y,z,u)$$ of the systems of equations

$\begin{cases} x+y=3(z+u), \\ x+z=4(y+u), \\ x+u=5(y+z). \\ \end{cases}$

What is the smallest value that $$x$$ can have?

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