If: \begin{eqnarray*} ax+by&=&m_1,\\ ax^2+by^2&=&m_2,\\ ax^3+by^3&=&m_3,\\ ax^4+by^4&=&m_4\\ &\vdots& \\ \end{eqnarray*} Where : $m_1,m_2,m_3,m_4$ are constants
What is the general formula for :$ax^n+by^n$
If: \begin{eqnarray*} ax+by&=&m_1,\\ ax^2+by^2&=&m_2,\\ ax^3+by^3&=&m_3,\\ ax^4+by^4&=&m_4\\ &\vdots& \\ \end{eqnarray*} Where : $m_1,m_2,m_3,m_4$ are constants
What is the general formula for :$ax^n+by^n$