IMO Shortlist 1967 problem 4
In what case does the system of equations
have a solution? Find conditions under which the unique solution of the above system is an arithmetic progression.
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In what case does the system of equations
$\begin{matrix} x + y + mz = a \\ x + my + z = b \\ mx + y + z = c \end{matrix}$
have a solution? Find conditions under which the unique solution of the above system is an arithmetic progression.
Source: Međunarodna matematička olimpijada, shortlist 1967
Školjka 
