Math Problem Solver

\[\left( {5}^{19} \right) \:\%\: 7 = 5\]

\[\begin{aligned}\left( {5}^{19} \right) \:\%\: 7& = 5^{19} \:\%\: 7\\& = 19073486328125 \:\%\: 7\\& = 5\end{aligned}\]

The notation \(m \% n\) denotes the remainder of the integer \(m\) divided by the integer \(n\). \(m \% n = r\) means that given integers \(m\) and \(n\), where \(n\) is non-zero, there exist integers \(q\) and \(r\), where \(\lvert r \rvert < \lvert n \rvert\), such that \(m = q n + r\). MathBot adopts the convention that the remainder \(r\) and the divisor \(n\) share the same sign. Alternate notations for \(m \% n\) are \(\operatorname{mod}(m, n)\) and \(m \bmod n\).