Indeterminate System of Linear Equations
Algebra
Level
3
Consider the system of equations
\[\begin{equation} \label{eq1} \begin{split} y & = 2{x}_{1}+{x}_{2} \\ y & = 3{x}_{2}+{x}_{3} \\ y & = 4{x}_{3}+{x}_{4} \\ y & = 5{x}_{4}+{x}_{5} \\ y & = 6{x}_{5}+{x}_{1}. \end{split} \end{equation}\]
If all of the variables are integers, what is the minimum positive integer value of
\[\left(\sum_{i=1}^{5}{x}_{i}\right) - y ?\]
by
Steven Zheng