Find the remainder when 24^50 - 15^50 is divided by 13.
I know that we'd have to simplify 24^50 and 15^50, but it's hard to do. Can anyone help me?
+26367 Find the remainder when \(24^{50} - 15^{50}\) is divided by \(13\).
\(\begin{array}{|rcll|} \hline && \mathbf{24^{50} - 15^{50} \pmod{13}} \quad | \quad 24 \equiv -2 \pmod{13},\ 15 \equiv 2 \pmod{13} \\ &\equiv& (-2)^{50} - 2^{50} \pmod{13} \\ &\equiv& 2^{50} - 2^{50} \pmod{13} \\ &\equiv& \mathbf{0 \pmod{13}} \\ \hline \end{array}\)
