Найдите все целые значения р, при которых уравнение x^2-рх-6=0 имеет целые корни.

\[x^{2} - px - 6 = 0\]

\[\left\{ \begin{matrix} x_{1} + x_{2} = - p \\ x_{1} \cdot x_{2} = q\ \ \ \ \ \\ \end{matrix}\text{\ \ \ \ \ \ \ \ } \right.\ \]

\[\left\{ \begin{matrix} x_{1} + x_{2} = - ( - p) = p\ \ \ \ \\ x_{1} \cdot x_{2} = - 6\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \\ \end{matrix} \right.\ \]

\[1 \cdot ( - 6) = ( - 1) \cdot 6 = 2 \cdot ( - 3) =\]

\[= ( - 2) \cdot 3 = - 6.\]

\[p_{1} = 1 + ( - 6) = 1 - 6 = - 5;\]

\[p_{2} = - 1 + 6 = 5;\]

\[p_{3} = 2 + ( - 3) = 2 - 3 = - 1;\]

\[p_{4} = - 2 + 3 = 1.\]

\[Ответ:\ \ \ \ p = \left\{ - 5;\ - 1;1;5 \right\}.\]