The values of $m , n$, for which the system of equations
\begin{align*}
x + y + z &= 4,\\
2x + 5y + 5z &= 17,\\
x + 2y + \mathrm{m}z &= \mathrm{n}
\end{align*}
has infinitely many solutions, satisfy the equation:\\
(1) $m ^ { 2 } + n ^ { 2 } - m n = 39$\\
(2) $m ^ { 2 } + n ^ { 2 } - m - n = 46$\\
(3) $m ^ { 2 } + n ^ { 2 } + m + n = 64$\\
(4) $m ^ { 2 } + n ^ { 2 } + m n = 68$