1963 IMO Problems/Problem 4

Problem

Find all solutions $x_1,x_2,x_3,x_4,x_5$ of the system

$\begin{eqnarray}x_5+x_2&=&yx_1\\x_1+x_3&=&yx_2\\x_2+x_4&=&yx_3\\x_3+x_5&=&yx_4\\x_4+x_1&=...$

where $y$ is a parameter.

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1963 IMO (Problems)
Preceded by Problem 3	1 • 2 • 3 • 4 • 5 • 6	Followed by Problem 5